Question

A tower casts a shadow that is 60 feet long when the angle of elevation of the sun is 65˚. How tall is the tower? Round answer to the nearest whole number correctly!

Answer 1

Answer: Tthe tower is 129 feet tall.

Step-by-step explanation:

According to trigonometry in a right triangle:

$\tan\theta =\dfrac{\text{Side opposite to }\theta}{\text{Side adjacent to }\theta}$

Let x be the height of the tower.

Given , $\theta=65^{\circ}$

Since tower stands vertical to the ground, that means it is making a right triangle with the shadow.

$\tan 65^{\circ}=\dfrac{x}{60}\\\\\Rightarrow\ 2.1445=\dfrac{x}{60}\ \ \text{[Using calculator]}\\\\\Rightarrow x= 2.1445\times60=128.67\approx129\text{ feet}$

Hence, the tower is 129 feet tall.