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.

Explanation:

According to trigonometry in a right triangle:

`\tan\theta =\frac{\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)=(x)/(60)\\\\\Rightarrow\ 2.1445=(x)/(60)\ \ \text{[Using calculator]}\\\\\Rightarrow x= 2.1445*60=128.67\approx129\text{ feet}`

Hence, the tower is 129 feet tall.