Question

A building 250 feet tall casts a 60 foot long shadow. If a person looks down from the top of the 1)_______ building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.)
A) 14
B) 77
C) 76
D) 13

Answer 1

Answer:

D) 13

Step-by-step explanation:

Let x represent our required angle.

Please find the attachment.

We have been given that a 250 feet tall building casts a 60 foot long shadow.

We can see from our attachment that 60 is opposite side and 250 is adjacent side to angle x. We also know that tangent relates opposite side of a right triangle with its adjacent side.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(x)=\frac{60}{250}$

$\text{tan}(x)=\frac{6}{25}$

Now, we will use arctan to solve for x as:

$x=\text{tan}^{-1}(\frac{6}{25})$

$x=13.49573328^{\circ}$

Round to nearest degree:

$x\approx 13^{\circ}$

Therefore, the measure of the angle between the end of the shadow and the vertical side of the building is 13 degrees.