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Chapter 3: Q. 402 (page 408)

In the following exercises, use the Pythagorean Theorem to find the length of the missing side. Round to the nearest tenth, if necessary.

Short Answer

Expert verified

The length of the missing side is 20.

Step by step solution

01

Step 1. Given Information 

We are given a right-angled triangle whose length of the hypotenuse is 25and length of one leg is 15.

The objective is to find the length of the missing side.

02

Step 2. Concept Used 

The Pythagorean Theorem states that in any right triangle, a2+b2=c2where c is the length of the hypotenuse anda andb are the lengths of the legs.

03

Step 3. Find the missing length 

As the length of the hypotenuse is 25and the length of one leg is 15, so in the equation a2+b2=c2substitute 25for cand 15for a.

152+b2=252225+b2=625b2=625-225b2=400

Taking square root both sides we get

b2=400b=20

So the length of the missing side is 20.

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