Chapter 10.6, Problem 38E

To determine

To find the unknown sides.

Answer to Problem 38E

  $x=26\sqrt{3}$ and y = 52 m

Explanation of Solution

Given Information: For angle $\theta =60°$

Perpendicular = x, Hypotenuse = y and Base = 26 m

Formula Used: $\tan \theta =\frac{Perpendicular}{Base}$ and $\cos \theta =\frac{Base}{Hypotenuse}$

Calculation:

Now Perpendicular x.

For angle $\theta =60°$

Perpendicular = x, Base = 26 m

  $\tan \theta =\frac{Perpendicular}{Base}$

Put value of Base and $\theta$ to find Perpendicular x.

  $\tan 60°=\frac{x}{26}$

So, $\tan 60°=\sqrt{3}$

Hence,

Perpendicular $x=26\sqrt{3}$ m

Now find Hypotenuse y.

For angle $\theta =60°$

Base = 26 m and Hypotenuse = y

  $\cos \theta =\frac{Base}{Hypotenuse}$

Put value of Base and $\theta$ to find Hypotenuse y

.

  $\cos 60°=\frac{26}{y}$

So, $\cos 60°=\frac{1}{2}$

Hence,

Hypotenuse r $y=26\times 2=52$ m