Chapter 8, Problem 21CR

To determine

To find: the value of y⁰

Answer to Problem 21CR

The value of y is $y=54°$

Explanation of Solution

Given Information: A right angled triangle with altitude of measure $13$ and hypotenuse of measure 24.

Formula used:

In a right triangle the cosine of the angle is the ratio of the measure of side adjacent to the angle to the hypotenuse.

  

It can be expressed as,

  $\cos B=\frac{b}{c}$

Calculation: Consider the right triangle given below.

  

Here, considering the triangle with y as the acute angle,

  $\begin{array}{c}\cos x°=\frac{13}{24}\\ x={\cos }^{-1}\left(\frac{13}{24}\right)\\ ={\cos }^{-1}\left(0.5416\right)\end{array}$ .

Referring to the table of trigonometric values in Page 311 in the textbook, the angle can be obtained as,

  $x=54°$