Question

Help!

A tree casts a 20-foot shadow when the sun makes an angle of 42 degrees with the ground. Find the height of the tree to the nearest foot.

Answer 1

18.8 feet

Explanation:

You have to use trigonometry for this question.

So, the basic measurements we have are:

1. The angle of elevation = 42 degrees

2. Base length of the triangle(ie. the shadow on the floor) = 20 ft

Now, imagine a right angled triangle with the base length as the shadow height, the height of the triangle as the height of the tree and the hypotenuse as the sun ray that causes the shadow. Also, the angle opposite the height is the 42 degrees.

So, we know the Adjacent length and we want to know the opposite length ( in respects with the angle given)

So, the trig ratio that compares the two is ‘Tan’

Now, form the equation:

Tan (42) = Opposite/ Adjacent = O/ A = O/20

Rearrange to solve:

O/20 = Tan(42)

O = Tan(42) x 20

Key these into a calculator and you get the answer: 18.800808...

Round to a suitable degree of accuracy.

18.8 ( 3s.f)