- Getting ready for right triangles and trigonometry
- Hypotenuse, opposite, and adjacent
- Side ratios in right triangles as a function of the angles
- Using similarity to estimate ratio between side lengths
- Using right triangle ratios to approximate angle measure
- Use ratios in right triangles
- Right triangles & trigonometry: FAQ
Right triangles & trigonometry: FAQ
Frequently asked questions about right triangles & trigonometry
What are the trigonometric ratios?
The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan). These are defined for acute angle below:
Triangle A B C with angle A C B being ninety degrees. Angle B A C is the angle of reference. Side B C is labeled opposide. Side A C is labeled adjacent. Side A B is labeled hypotenuse.
In these definitions, the terms opposite, adjacent, and hypotenuse refer to the lengths of the sides.
Learn more with our Trigonometric ratios in right triangles video.
Practice with our Trigonometric ratios in right triangles exercise.
Where are these topics used in the real world?
Trigonometry is used in a lot of different fields! Architects and engineers use trigonometry to design buildings and bridges. Surveyors use it to measure distances and angles. Astronomers use trigonometry to measure distances between stars and galaxies. In addition, carpenters, artists, and even athletes can use the principles of right triangle trigonometry in their work.
What do we know about the sine and cosine of complementary angles?
Knowing the sine and cosine of complementary angles can be helpful when solving problems with right triangles. The sine of an angle is equal to the cosine of its complementary angle, and vice versa. So if we know the cosine of an angle, we can use that information to find the sine of its complementary angle, or vice versa.
Practice with our Relate ratios in right triangles exercise.
How do we use the reciprocal trigonometric ratios?
The reciprocal trigonometric ratios are just the inverses of the regular trigonometric ratios: cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent. We can use them in the same way we use the regular trigonometric ratios, to solve for side lengths or angles in right triangles.
Practice with our Reciprocal trig ratios exercise.
What do we mean by modeling with right triangles?
We can use right triangles to model real-world situations. For example, we might use a right triangle to figure out the height of a building or the distance across a river. Modeling with right triangles can help us solve problems we wouldn't be able to solve otherwise.
Practice with our Right triangle trigonometry word problems exercise.
Want to join the conversation?
- All the boring uses. "Where do I put this thing?"
Meanwhile there are people creating harmonic distortion or digital filters with trig, and the discrete cosine transform is the core of JPEG encoding. We could have banned nuclear bombs, but we didn't have a way to detect underground testing when we got together for that treaty—noticing that MANY of the multiplications are the same because sine waves cross or are opposites at lots and lots of points solved that problem, but a bit too late, otherwise we'd have been picking apart the signals from seismographs and looking for indicators of underground nuclear detonations, along with enough information to know exactly where they were happening.(6 votes)
- ?this doesnt make any sense(4 votes)
- how do you do inverse functions?(4 votes)
- how do you do inverse function?(4 votes)
- Where in a situation do you need to inverse functions, ps I’m only 9yrs old and already doing algebra and now trigonometric ratios : D(1 vote)
- I'm 10 yrs old and doing this(4 votes)
- What is the hypotenuse from ∠c's perspective?
Thanks in advance.(1 vote)
- The hypotenuse of a right angle is simply that, the hypotenuse, regardless of any particular angles “perspective”. It is never (as I understand it) considered the “adjacent” or “opposite” side; it is only considered the “hypotenuse” side.(2 votes)
- how do you inverse a function backwards, or if a function is already inverse, how do you make it normal again?(1 vote)
- "The reciprocal trigonometric ratios are just the inverses of the regular trigonometric ratios:"
Wrong, please stop equating the word 'reciprocal' with the word 'inverse'. They are not interchangeable terms.(1 vote)
- PPs I’m on my dad’s laptop(1 vote)
- Does anyone know what the atan function stands for?(1 vote)
- tan is for opposite over adjacent in a right triangle like you & me saw in the last exercise.(1 vote)