Question

Kelsea and Landon are playing in a park standing 100 feet away from each other. They both see a bird flying above them. The angles of elevation from each person to the bird are shown. How high is the bird from the ground? Round your answer to the nearest tenth. The angle for landon is 45 degrees the angle for kelsea is 20

Answer 1

26.68 ft

Explanation:

Let a represent the distance from Kelsea to the bird and b be the distance from Landon to the bird.

Let x = angle of the bird. Hence:

x + 45 + 20 = 180 (sum of angles in a triangle)

x + 65 = 180

x = 180 - 65

x = 115°

Using sine rule:

`(100\ ft)/(sin(115)) =(a)/(sin(45)) =(b)/(sin(20)) \\\\(100\ ft)/(sin(115)) =(a)/(sin(45))\\\\a=(100\ ft)/(sin(115)) *sin(45)\\\\a=78\ ft\\`

Let h = height of the bird to the ground. Since a right angle is formed. hence:

`(h)/(sin(20)) =(78)/(sin(90)) \\\\h=(78)/(sin(90))*sin(20)\\\\h=26.68\ ft`