# How to find the hypotenuse of a triangle with only one side

Also be on the lookout for multiples like and 2. In a right triangle, the hypotenuse will always be the longest side, so here it must be 17 yards.

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Trig ratios sine, cosine, tangent. We're asked to solve the right triangle shown below. Give the links to the nearest tenth. So when they say solve the right triangle, we can assume that they're saying, hey figure out the lengths of all the sides.

So whatever a is equal to, whatever b is equal to. And also what are all the angles of the right triangle?

### The Pythagorean Theorem

They've given two of them. We might have to figure out this third right over here.

So there's multiple ways to tackle this, but we'll just try to tackle side XW first, try to figure out what a is. And I'll give you a hint.

You can use a calculator, and using a calculator, you can use your trigonometric functions that we've looked at a good bit now. So I'll give you a few seconds to think about how to figure out what a is. Well, what do we know? We know this angle y right over here. We know the side adjacent to angle y. And length a, this is the side that's the length of the side that is opposite to angle Y.

So what trigonometric ratio deals with the opposite and the adjacent? So if we're looking at angle Y, relative to angle Y, this is the opposite. And this right over here is the adjacent.

Well if we don't remember, we can go back to SohCahToa. Sine deals with opposite and hypotenuse.

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Solve a Right Triangle Given an Angle and the HypotenuseJoin them; it only takes a minute: Finding a square root takes some practice, but it also takes knowledge of multiplication, division, and a little bit of trial and error. Look at the table below. Number y which, when multiplied by itself, equals number x. If you can remember those square numbersâ€”or if you can use a calculator to find themâ€”then finding many common square roots will be just a matter of recall. For which of these triangles is? This is not a right triangle, so you cannot use the Pythagorean Theorem to find r.

The correct answer is Triangle B. This is a right triangle; when you sum the squares of the lengths of the sides, you get the square of the length of the hypotenuse. Finding the Length of a Leg. Consider the example below. Find the length of side a in the triangle below. Use a calculator to estimate the square root to one decimal place. In this right triangle, you are given the measurements for the hypotenuse, cand one leg, b.

## Finding a Side in a Right-Angled Triangle

The hypotenuse is always opposite the right angle and it is always the longest side of the triangle. To find the length of leg asubstitute the known values into the Pythagorean Theorem. Solve for a 2.

Use a calculator to find the square root of The calculator gives an answer of 3. Since you are approximating, you use the symbol.

Which of the following correctly uses the Pythagorean Theorem to find the missing side, x? All of the functions can be rearranged using this method. To make the next chart easier to read, the terms have been placed in a different order.

This chart will be referred to as the NAK chart. The NAK chart shows which functions of the angle should be multiplied by the known side to get the needed side. Use the NAK chart if you know one angle other than the right angle and the length of one side.

Determine your knowns and needs.