https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/v/basic-trigonometry-ii 2021-06-30T17:32:36Z Trigonometric ratios in right triangles Sal shows a few examples where he starts with the two legs of a right triangle and he finds the trig ratios of one of the acute angles. Sal Khan video https://cdn.kastatic.org/googleusercontent/cwpGy84NzSmhKdw05CgXGtrk00QP2OcirhTztXczYdrISg6awjAEHFhgQLuF8VUYPmXsM-LOJBMBVSmZ3yP555zf Trigonometric ratios in right triangles Sal shows a few examples where he starts with the two legs of a right triangle and he finds the trig ratios of one of the acute angles. https://cdn.kastatic.org/ka-youtube-converted/G-T_6hCdMQc.mp4/G-T_6hCdMQc.mp4 731 Basic trigonometry https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/a/finding-trig-ratios-in-right-triangles 2022-09-10T02:03:40.164764806Z Trigonometric ratios in right triangles Learn how to find the sine, cosine, and tangent of angles in right triangles. article https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-pyth-theorem/a/getting-ready-for-right-triangles-and-trigonometry 2026-03-26T05:50:46.505911114Z Getting ready for right triangles and trigonometry Practicing finding right triangle side lengths with the Pythagorean theorem, rewriting square root expressions, and visualizing right triangles in context helps us get ready to learn about right triangles and trigonometry. article https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-trig-ratios-intro/e/trigonometry_1 2026-04-01T11:24:50.133517701Z Trigonometric ratios in right triangles Given the side lengths of a right triangle, find the sine, cosine, or tangent of one of the acute angles. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-trig/xff63fac4:hs-geo-trig-ratios-similarity/a/opposite-adjacent-hypotenuse 2022-09-10T02:03:40.164764806Z Hypotenuse, opposite, and adjacent In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. article https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles/xfefa5515:ratios-in-right-triangles/a/right-triangles-trigonometry-faq 2023-01-05T23:53:38.038529637Z Right triangles & trigonometry: FAQ Frequently asked questions about right triangles & trigonometry article https://www.khanacademy.org/math/ka-math-class-9/x152b0968b8680a8d:heron-s-formula-ncert-new/x152b0968b8680a8d:area-of-triangle-by-heron-s-formula/v/herons-formula-indian-accent 2025-06-10T04:38:32.202755958Z Heron's formula Using Heron's Formula to determine the area of a triangle while only knowing the lengths of the sides. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by Kalakrit (Dubbing) video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Heron's formula Using Heron's Formula to determine the area of a triangle while only knowing the lengths of the sides. Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now! Khan Academy India is a nonprofit organization with the mission of providing a free, world-class education for anyone, anywhere. We have videos and exercises that have been translated into multiple Indian languages, and 15 million people around the globe learn on Khan Academy every month. Support Us: https://india.khanacademy.org/donate Created by https://cdn.kastatic.org/ka-youtube-converted/IMlCEGwIto0.mp4/IMlCEGwIto0.mp4 283 Basic trigonometry https://www.khanacademy.org/math/ka-math-class-9/x152b0968b8680a8d:heron-s-formula-ncert-new/x152b0968b8680a8d:area-of-triangle-by-heron-s-formula/e/understanding-heron-s-formula 2024-06-10T11:27:45.483509161Z Understanding Heron's formula This exercise is a replica of 10.1 exercise which was do-all, now this is curated for new ncert and is do-4 Devashish Phadnis exercise https://www.khanacademy.org/math/class-9-geometry-od/x0a98afb01410c41a:mensuration/x0a98afb01410c41a:area-of-triangles/e/finding-area-of-triangle-using-heron-s-formula 2026-03-07T07:20:41.87360937Z Finding area of triangle using Heron's formula part 1 We will find the area of triangle using Heron's formula. anmol exercise https://www.khanacademy.org/math/ka-math-class-9/x152b0968b8680a8d:heron-s-formula-ncert-new/x152b0968b8680a8d:area-of-triangle-by-heron-s-formula/e/finding-area-of-triangle-part-2 2024-05-16T12:18:34.840009131Z Finding area of triangle part 2 Using herons formula a little difficult problem. Devashish Phadnis exercise https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/v/example-trig-to-solve-the-sides-and-angles-of-a-right-triangle 2021-06-30T17:32:38Z Solving for a side in right triangles with trigonometry Sal is given a right triangle with an acute angle of 65° and a leg of 5 units, and he uses trigonometry to find the two missing sides. Sal Khan video https://cdn.kastatic.org/googleusercontent/X0ECxxkRbmZu7H78vm4EbH8BRKYqPBGlzkuAdFqDsmG5d33yLEW3qY54S02C0-YF6OUMI-SPnXfHJYAyuzICHfCYJQ Solving for a side in right triangles with trigonometry Sal is given a right triangle with an acute angle of 65° and a leg of 5 units, and he uses trigonometry to find the two missing sides. https://cdn.kastatic.org/ka-youtube-converted/l5VbdqRjTXc.mp4/l5VbdqRjTXc.mp4 424 Basic trigonometry https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-a-side/a/unknown-side-in-right-triangle-w-trig 2025-02-11T16:42:34.189704851Z Solving for a side in right triangles with trigonometry Learn how to use trig functions to find an unknown side length in a right triangle. article https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-solve-for-an-angle/e/solve-for-an-angle-in-a-right-triangle 2024-09-04T17:59:01.633715485Z Solve for an angle in right triangles Given two sides in a right triangle, find one of the acute angles using trigonometry. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/v/angle-to-aim-to-get-alien 2021-06-30T17:32:40Z Right triangle word problem Sal solves a modeling problem where he finds the necessary angle to shoot at a vicious alien. Sal Khan video https://cdn.kastatic.org/googleusercontent/dlKu1szoXgEqwAoKxoMQLwa9LQVPo-o5Xt6xJ7m4NixSAhQDy0ixvWC3z9NTDTrLNi4qYlA-wQGTGhmRy0ab_ypT Right triangle word problem Sal solves a modeling problem where he finds the necessary angle to shoot at a vicious alien. https://cdn.kastatic.org/ka-youtube-converted/aHzd-u35LuA.mp4/aHzd-u35LuA.mp4 275 Basic trigonometry https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/e/applying-right-triangles 2026-05-06T06:30:43.913440672Z Right triangle trigonometry word problems Solve word problems by modeling real-world (and not-so-real) situations as right triangles and using trigonometry. Tomer Gal exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:law-of-sines/v/law-of-sines 2021-04-07T10:59:31Z Solving for a side with the law of sines Sal is given a triangle with two angle measures and one side length, and he finds all the missing side lengths and angle measures using the law of sines. Sal Khan video https://cdn.kastatic.org/googleusercontent/GmsMqH6JAQGiI8UTxS51OHzToylI3__kF-tIMpRpAGDMBMQBe76Fb1_c_4hV044l-HlIeVrCgbtD_xUTGfQdL6A Solving for a side with the law of sines Sal is given a triangle with two angle measures and one side length, and he finds all the missing side lengths and angle measures using the law of sines. https://cdn.kastatic.org/ka-youtube-converted/VjmFKle7xIw.mp4/VjmFKle7xIw.mp4 358 Basic trigonometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:law-of-sines/v/law-of-sines-example 2021-04-07T10:59:32Z Solving for an angle with the law of sines Sal is given a triangle with two side lengths and one angle measure, and he finds all the missing angle measures using the law of sines. Sal Khan video https://cdn.kastatic.org/googleusercontent/qwvf9pjvkpngEnhmmlymiBn3jpSL5B0gZI-qTn-FJoUCAWHg8p4a26XIcXDWTPLvuUXJAnxxSGjzk8l0-SnXmT6k Solving for an angle with the law of sines Sal is given a triangle with two side lengths and one angle measure, and he finds all the missing angle measures using the law of sines. https://cdn.kastatic.org/ka-youtube-converted/IJySBMtFlnQ.mp4/IJySBMtFlnQ.mp4 334 Basic trigonometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:law-of-sines/v/proof-law-of-sines 2021-04-07T10:59:32Z Proof of the law of sines Sal gives a simple proof of the Law of sines. Sal Khan video https://cdn.kastatic.org/googleusercontent/qPevnSJjmA6PDrrpXLADgHx7ZFVepyfd4fbB2rO4DGIyHJccxkd9Vg8B1Ki79pZuS3v__hG5PHZKe4L4AcSbwNGvVQ Proof of the law of sines Sal gives a simple proof of the Law of sines. https://cdn.kastatic.org/ka-youtube-converted/APNkWrD-U1k.mp4/APNkWrD-U1k.mp4 394 Basic trigonometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:law-of-sines/e/law_of_sines 2026-03-26T05:20:35.16058035Z Solve triangles using the law of sines Find missing triangle measures using the law of sines. Ben Eater exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:law-of-cosines/v/law-of-cosines-example 2021-04-07T10:59:30Z Solving for a side with the law of cosines Learn how to use the law of cosines to find the missing side length of a triangle when given two side lengths and the contained angle measure. Sal Khan video https://cdn.kastatic.org/googleusercontent/DaAhZigTYTg0jYhdeNQusud7XfeHWCiT4KFff-g-r45ngAWWdtK3wk1FZDriWv-_ls8jOcaLREx2oq5g67wjAJcp Solving for a side with the law of cosines Learn how to use the law of cosines to find the missing side length of a triangle when given two side lengths and the contained angle measure. https://cdn.kastatic.org/ka-youtube-converted/ZElOxG7_m3c.mp4/ZElOxG7_m3c.mp4 278 Basic trigonometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:law-of-cosines/v/law-of-cosines-missing-angle 2021-04-07T10:59:29Z Solving for an angle with the law of cosines Sal is given a triangle with all side lengths but no angle measure, and he finds one of the angle measures using the law of cosines. Sal Khan video https://cdn.kastatic.org/googleusercontent/0ssPaOePflPJ5nkwPeo0o23fvVY1ncxcrvuRqiLqWjC0rR4FEcnDK3OcmUgCszkW0y51gYjj49BoDAbpGP03UWSf Solving for an angle with the law of cosines Sal is given a triangle with all side lengths but no angle measure, and he finds one of the angle measures using the law of cosines. https://cdn.kastatic.org/ka-youtube-converted/Ei54NnQ0FKs.mp4/Ei54NnQ0FKs.mp4 401 Basic trigonometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:law-of-cosines/v/law-of-cosines 2021-04-07T10:59:32Z Proof of the law of cosines Sal gives a simple proof of the Law of cosines. Sal Khan video https://cdn.kastatic.org/googleusercontent/_f9hFTK3K9UHO0aYaMaiYYJqx3IgTCbEbDgxgE3cAzSUWYLWlbS4uaJcC0X1XCP15uKn53A4Y0Ibg4BX7Fih3x0 Proof of the law of cosines Sal gives a simple proof of the Law of cosines. https://cdn.kastatic.org/ka-youtube-converted/pGaDcOMdw48.mp4/pGaDcOMdw48.mp4 566 Basic trigonometry https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:solving-general-triangles/a/laws-of-sines-and-cosines-review 2025-09-04T23:00:51.976854155Z Laws of sines and cosines review Review the law of sines and the law of cosines, and use them to solve problems with any triangle. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:law-of-cosines/e/law_of_cosines 2026-03-24T23:41:07.080866137Z Solve triangles using the law of cosines Solve missing triangle measures using the law of cosines. Ben Eater exercise https://www.khanacademy.org/math/9th-grade-math-revised-k-to-10-3-terms/x1e64c39423990571:3rd-quarter/x1e64c39423990571:trigonometric-ratios/v/intro-to-heights-and-distances 2020-08-19T18:08:11Z Intro to heights and distances Let's get introduced to heights and distances. Let's learn the meaning of the terms - 'line of sight', 'angle of elevation', and 'angle of depression'. Aanand Srinivas video https://cdn.kastatic.org/googleusercontent/rou31Q6o1bYVnUOnOffSv4-ikH4zYKR6PEk51p7ZS5yKyqSqwiNqKoUlTT4CP4jttDCT01YiXmSmf7ixbwSfbPMA Intro to heights and distances Let's get introduced to heights and distances. Let's learn the meaning of the terms - 'line of sight', 'angle of elevation', and 'angle of depression'. https://cdn.kastatic.org/ka-youtube-converted/TgQs7k5p2Ag.mp4/TgQs7k5p2Ag.mp4 767 Basic trigonometry https://www.khanacademy.org/math/geometry/hs-geo-trig/hs-geo-modeling-with-right-triangles/a/angles-of-elevation-and-depression 2022-09-10T02:03:40.164764806Z Angles of elevation and depression Learn what  the terms angle of elevation and angle of depression mean. The words may be big but their meaning is pretty basic! article https://www.khanacademy.org/math/revision-term-1-ncert-math-class-10/x2f82315bf1a14434:week-2/x2f82315bf1a14434:some-applications-of-trigonometry/e/word-problems--one-triangle-involved 2026-05-12T22:10:47.015864082Z Word problems: one triangle involved Let's practice some word problems that involve applications of trigonometry in a single triangle. ashish exercise https://www.khanacademy.org/math/revision-term-1-ncert-math-class-10/x2f82315bf1a14434:week-2/x2f82315bf1a14434:some-applications-of-trigonometry/e/word-problems--two-triangles-involved 2026-03-08T08:10:35.408394002Z Word problems: two triangles involved Let's practice some challenging word problems that involve applications of trigonometry. ashish exercise https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/v/pythagorean-theorem-3 2023-06-02T19:09:07.369858129Z Pythagorean theorem word problem: carpet If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet. Sal Khan video https://cdn.kastatic.org/googleusercontent/yu5zzccGvx1c9EkgqD5u-SX3Qt42CJ2BRnvfLfSYtExN8xzpTmsAD64vGZz5qoGjBvup3ST8TRsu258UWRd_mF0 Pythagorean theorem word problem: carpet If we draw the diagonal on a rectangular carpet, then its length, width, and diagonal form a right triangle. Since we know the length and diagonal measurements, we can use the Pythagorean theorem to solve for the missing width of the carpet. https://cdn.kastatic.org/ka-youtube-converted/T0IOrRETWhI.mp4/T0IOrRETWhI.mp4 180 Basic trigonometry https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/pythagorean-theorem-application/e/pythagorean-theorem-word-problems--basic 2026-03-31T14:59:02.026924717Z Pythagorean theorem word problems Use the Pythagorean theorem to solve word problems. Lindsay exercise