Question

A pole is $20$ feet high. A taut wire that is $46$ feet extends from the top of the pole to the ground. What is the angle of depression, to the nearest degree, from the top of the pole to the bottom of the wire?

• A. $23$
• B. $26$
• C. $43$
• D. $64$
• E. $67$

Answer 1

Answer: (B)

$26$

The given setup will form a right angled triangle with hypotenuse length $46$ feet and height of pole is $20$ fee

Let the angle of depression be $\alpha$

$\because \sin \alpha =\frac{opposite}{hypotenuse}$

$\therefore$ Angle of depression $=\alpha ={\sin }^{-1}\left(\frac{20}{46}\right)=26°$

Hence, the angle of depression is ${26}^o$