Question

The sun is 21° above the horizon. It makes a 54 m -long shadow of a tall tree. How high is the tree? Express your answer in meters.

Answer 1

Height of the tree, h = 20.72 meters

Step-by-step explanation:

Given that,

The sun is 21° above the horizontal,
`\theta=21^(\circ)`

Length of the shadow, d = 54 m

Let h is the height of the tree. It can be calculated using trigonometry as :

`tan\theta=(perpendicular)/(base)`

Here, perpendicular is h and base is 54 meters.

`tan(21)=(h)/(54)`

`h=tan(21)* 54`

h = 20.72 meters

So, the height of the tree is 20.72 meters. Hence, this is the required solution.