Chapter 8, Problem 15CR

To determine

To find : the value of x

Answer to Problem 15CR

The value of x is $x=16$

Explanation of Solution

Given Information: Two right angled triangles with common altitude of measure $8\sqrt{3}$ .Each triangle has an acute angle of 60⁰ which is opposite to the altitude.

Formula used:

In a right triangle the sine of the angle is the ratio of the measure of side opposite to the angle to the hypotenuse.

  

It can be expressed as,

  $\sin B=\frac{a}{c}$

Calculation: Consider the right triangle given below.

  

Here, considering the triangle with x as the hypotenuse.

  $\begin{array}{c}\sin 60°=\frac{8\sqrt{3}}{x}\\ x=\frac{8\sqrt{3}}{\sin 60°}\\ =\frac{8\sqrt{3}}{\left(\sqrt{3}/2\right)}\\ =16\end{array}$ .

It can be observed that, the hypotenuse of the second triangle also measures 16 units since the angle is same and the altitude is common to both triangles.