Question

Madera's mayor is watching a car from the ledge of the water tower. The car is directly approaching the water tower. When first noticed, the angle of depression to the car is 58°. When the car stops, the angle of depression is 77°. The mayor's line of sight is 127 feet above the ground.

Part 1

How far did the car travel from when it was first noticed until it stopped? Round to the nearest foot. 

The car traveled ___________ feet from when it was first noticed until it stopped.

Part 2

Explain how you determined the distance the car had traveled by applying your understanding of the angles and the height of the mayor standing on top of the water tower. 

Answer 1

Solution:

I) We should find the distance at each given angle:

1) $\frac{127}{tan(58\degree)}=79.36 ft$

2) $\frac{127}{tan(77\degree)}= 29.32ft$

In order to find the distance car travel from when it was first noticed until it stopped:

79.36 - 29.32 = 50.04 feet

Answer: 50 feet

II) The type of math it's using is trigonometric ratios and Pythagoras theorem.