Question

A bird watcher spied a woodpecker. The bird watcher is 40 yards lower than the woodpecker. The distance from the bird watcher to the woodpecker is 175 yards. What is the angle of elevation?

a. 12.9°
b. 13.2°
c. 76.8°
d. 77.1°

Answer 1

H = 40, D = 175 where H is the height and D is the distance

tan(x) = 40/175

x = arctan(40/175) = 12.88 degrees

Rounded up: 12.9

Answer 2

Option: b is the correct answer.

b. 13.2°

Explanation:

This problem can be modeled with the help of a right angled triangle and let the angle of elevation be θ.

Also, the side opposite to angle θ is: 40 yards.

and the hypotenuse of the right triangle is: 175 yards.

Hence, In right angled triangle i.e. ΔABC is:

`\sin \theta=(40)/(175)\\\\i.e.\\\\\sin \theta=0.22857`

i.e.

`\theta=\arcsin (0.228571)\\\\i.e.\\\\\theta=13.2129\ degree`

i.e.

The angle of elevation is: 13.2°