Question

You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the ground and use trig to calculate the height.

The shadow measures 500 feet and you calculate the angle of elevation to be 35 degrees, This forms a right triangle.
a. What is the measure of the other acute angle?
b. What is the height of the tree?
c. You are standing at the end of the tree's shadow and want to take a picture of the tree but your camera can only focus at distance less than 500 feet. When you hold the camera to take the picture it is 5 feet above the ground. What is the distance from the end of the shadow to the top of the tree?
d. Can you take a clear picture of the top of the tree from where you are standing?
e. How many total tiles will be needed to complete the job?

Answer 1

Explanation:

given that You are visiting a Redwood tree forest and want to verify the height of one of the trees. You measure its shadow along the ground and use trig to calculate the height.

the shadow measures 500 feet and you calculate the angle of elevation to be 35 degrees, This forms a right triangle.

a) Other acute angle is 90-35 = 55 degrees

b) Height of the tree = 500 tan 35 =350.104 feet

c) Here height would be reduced to 350.104 - 5 = 345.104 feet.

Hence distance adjusted= 354.104 cot 35=492.8596 feet.

d) Yes because this is less than 500 feet.

e) height of 5 feet itself is sufficient here