   Chapter 8.5, Problem 44E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In ∆ A B C ,   m ∠ C = 90 ° and m ∠ B = 60 ° . If A B = 12 in., find the radius of the inscribed circle. Give the answer to the nearest tenth of an inch.

To determine

To find:

The length of radius of inscribed circle.

Explanation

Formula:

Radius of inscribed circle for right angled triangle:

If a, b and c are the lengths of sides of right angled triangle (c is the length of hypotenuse), then the length of radius r of circle inscribed in a right angled triangle is r=aba+b+c.

Sine ratio:

In a right angled triangle, sine of an angle θ is given by:

sinθ=opp(θ)hypotenuse

Where opp(θ) means the length of side opposite to θ.

Calculation:

Let’s find the length of AC using sine ratio.

sin 60°=ACAB

We know that sin 60°=32

So, let’s substitute the value of sin 600 and AB to find the value of AC.

32=AC12

AC=12×32=63 in.

Now, let’s use Pythagoras theorem to find the length of side BC

AB2=AC2+BC2.

122=632+BC2

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