Question

Jacob is standing 112 m from a building. The angle of elevation from where he is standing on the ground to the top of the building is 62°.

How tall is the building?

Answer 1

Answer:

Jacob is standing 112 m from a building. The building is 210.64 meters tall

Solution:

Given that Jacob is standing 112 meter from the building. Angle of elevation from where he is standing on the ground to the top of the building is 62 degrees

The figure for this sum is attached below

Consider below figure where point B represents Base of the building.

Point T represents top of the building  

Point J represents position of Jacob on the ground.

From given information  

TB is height of the building which need to be calculated.

BJ is distance of Jacob from the building that means BJ = 112 meters

$\text { Angle of elevation that is } \angle \mathrm{TJB}=62^{\circ}$

Treating TBJ as right angled triangle right angle at B.

$\tan x=\frac{\text { perpendicular }}{\text { base }}$

$\text { Tan of } \angle T J B=\frac{T B}{B J}$

$=>\tan \left(62^{\circ}\right)=\frac{T B}{B J}$

$\begin{array}{l}{=>\mathrm{TB}=\mathrm{B} \mathrm{J} \tan \left(62^{\circ}\right)} \\ {=>\mathrm{TB}=112 \times 1.8807} \\ {=>\mathrm{TB}=210.64 \mathrm{meters}}\end{array}$

Hence height of the building is 210.64 meters