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Pythagorean theorem word problem: fishing boat

Sal uses the Pythagorean theorem to solve a word problem about a fishing boat. Created by Sal Khan and Monterey Institute for Technology and Education.

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• Does the Pythagorean theorem only work on right triangles?
• Good question!

Draw a right-angled triangle, with a square drawn on each of the sides. The areas of the two smaller squares, added together, is equal to the area of the largest square.

Now draw two more triangles. In the first one, keep the longest side the same, but make the two shorter sides a bit shorter than in your first triangle. They will meet at an angle greater than 90°. Can you see that the areas of the squares drawn on their sides will add up to less than before? In the next triangle, keep the longest side the same, but make the two shorter sides a bit longer than in your first triangle. They will meet at an angle less than 90°. Can you see that the areas of the squares drawn on their sides will add up to more than before?

It is only when the two shorter sides meet at 90° do you get the relationship between the areas of the squares.

• Does it matter what order you pit the a2 or b2
• In the equation, no it does not because the terms are being added together. This is called the commutative property. In math we write the terms in alphabetical order according to the letter. That is why you see a2 written first, because a is before b in the alphabet.
On the triangle, as long as you are using the smaller sides of the triangle, called legs, it does not matter which you label as a or b.
• What if the mast isn't absolutely upright? How would we find the length of the rope then?
• If it isn't a right triangle you will need to use the Law of Cosines, or the Law of Sines.
• how is the Pythagorean useful in word problems?
• It you need to find the length of a ladder on the side of a house, which makes a right triangle
• Is there another theorem for other types of triangles?
• There are several theorems relating the sides and angles of general triangles. Try the Law of Sines and Law of Cosines in the Trigonometry section.
• can someone help? i have a hard time converting the answers in the modules.
• Try finding the lengths first before you calculate anything and make sure to draw a triangle so it makes it alot easier for yourself!
(1 vote)
• Is there any theorems for the other types of triangles (scalene, equalateral) like there is the Pythagorean theorem?
(1 vote)
• Most of the times no but in some unique cases yes
• is Pythagoras theorem is the root of trigonometry?
why is there a need for Pythagoras theorem?
• In a sense, creation of the unit circle is based on the Pythagorean theorem, but it you have a right angle and the measure of two sides without knowing the angles, the Pythagorean theorem is the quickest way of finding the third side (and most accurate) without having to go through trig functions to find angles.