Question

A flagpole 95.2 ft. Tall is on top of a building. From a point on level ground, the angle of elevation of the top of the flagpole is 34.1° , while the angle of elevation of the bottom of the flagpole is 25.8° . Find the height of the building.

Answer 1

Let x be the height of the building

We will first make a sketch

$\tan \theta=\frac{opposite}{\text{adjacent}}$$\tan 25.8=\frac{x}{y}$

$y=\frac{x}{\tan 25.8}$$\tan 34.1=\frac{95.2+x}{y}$

substitute the y-value in the above

$\tan 34.1=\frac{95.2+x}{\frac{x}{\tan 25.8}}$$\tan 34.1=(95.2+x)\text{.}\frac{tan25.8}{x}$$x\tan 34.1=(95.2+x)\tan 25.8$

x (0.677) = (95.2 + x)0.4834

open the parenthesis

0.677x = 46.01968 + 0.4834x

subtract 0.4834x from both-side of the equation

0.677x - 0.4834x = 46.01968

0.1936x = 46.01968

Divide both-side by 0.1936

x≈ 237.7 ft

$x\approx238\text{ f}eet$