A skyscraper is 396 meters tall. At a certain time of day, it casts a shadow that is 332 meters long. At what angle is the sun above the horizon at that time?

Question

asked Aug 24, 2017 158k views

2 Answers

Fried Hoeben · Answer 1 · 2017-08-30T11:47:21+0000

Answer:

The sun is at an angle of 50.02° above the horizon at that time.

Explanation:

A skyscraper is 396 meters tall. At a certain time of day, it casts a shadow that is 332 meters long.

From the given attachment, in the right angled triangle ABC, AC is the skyscraper and BC is its shadow.

The angle that the sun is above the horizon is the angle of elevation or ∠B.

We know that,

$\tan \theta=(p)/(b)$

Putting the values,

$\Rightarrow \tan B=(AC)/(BC)$

$\Rightarrow \tan B=(396)/(332)$

$\Rightarrow B=\tan^(-1)(396)/(332)$

$\Rightarrow B=50.02^(\circ \:)$