Question

The angle of elevation of the top of a tower which is incomplete at a point 120 ft. from its base is 45. If the elevation at the same point of the top is desired to be 60 then the tower should be raised by 120 $(\sqrt{3}-1)$ ft.

• A. True
• B. False

Answer 1

The correct option is A True

Let $AB$ is the height of the tower and $AC$ be the raise in height of the tower

Let $AB=h,AC=x,\angle APB={45}^{\circ },\angle BPC={60}^{\circ }$

In $△BPC,\tan {60}^{\circ }=\frac{x+h}{120}$

$⟹x=120\sqrt{3}-h$

In $△BPA,\tan {45}^{\circ }=\frac{h}{120}$

$⟹h=120$

So $x=120\sqrt{3}-120=120(\sqrt{3}-1)\text{ft}$

The tower should be raised by $120(\sqrt{3}-1)$