Question

Artie's dad's house is 21 ft tall. If Artie's dad is at the top of the house installing shingles, and his son Artie is on the ground 12 ft away from the base of his dad's house, what is the angle of depression from the top of the house to the spot where Artie is standing?
A. 46.56
B. 60.26
C. 161.62
D. 11.65

Answer 1

Answer:

B. 60.26°

Step-by-step explanation:

Given:

Consider the diagram representing the above scenario.

The top of the house where dad is standing is at A. The point where his son is standing is B. The bottom of the house is at C. AC is the height of house, BC is the distance between the house and son.

Height of the house (AC) = 21 ft

Distance between the house and son (BC) = 12 ft

Let the angle of depression for the dad be 'x'.

From the figure, it is clear that,

Angle of depression of the dad will be same as angle of elevation of Artie.

For triangle ABC,

$\tan x=\frac{AC}{BC}\\\\\tan x=\frac{21\ ft}{12\ ft}\\\\\tan x=1.75\\\\x=\tan^{-1}(1.75)\\\\x=60.26$

Therefore, the angle of depression  from the top of the house to the spot where Artie is standing is 60.26°.

Therefore, the correct option is option (B).