Question

The petronas towers in Kuala Lumpur, Malaysia, are 452 meters tall. A woman who is 1.75 meters tall stands 120 meters from the base of one tower. Find the angle of elevation between the woman’s hat and the top of the tower. Round to the nearest tenth.

Answer 1

Answer:

$75.1^{\circ}$

Step-by-step explanation:

In this problem, we have:

H = 452 m is the height of the Petronas tower

h = 1.75 m is the height of the woman

d = 120 m is the distance between the woman and the base of the tower

First of all, we notice that we want to find the angle of elevation between the woman's hat the top of the tower; this means that we have consider the difference between the height of the tower and the height of the woman, so

$H' = H-h = 452-1.75=450.25 m$

Now we notice that $d$ and $H'$ are the two sides of a right triangle, in which the angle of elevation is $\theta$. Therefore, we can write the following relationship:

$tan \theta = \frac{H'}{d}$

since

H' represents the side of the triangle opposite to $\theta$

d represents the side of the triangle adjacent to $\theta$

Solving the equation for $\theta$, we find the angle of elevation:

$\theta = tan^{-1}(\frac{H'}{d})=tan^{-1}(\frac{450.25}{120})=75.1^{\circ}$