Question

1. A tree is making a 12 m shadow on the ground, the angle of elevation is 30 degrees, what is the height of the tree?

Answer 1

6.9m

Step-by-step explanation:

The situation can be represented as follows;

The height of the tree is x;

The shadow which is 12m on the ground has the horizontal component

The angle of elevation Θ is 30°

|\

| \

| \

x | \

| \

| 30°( \

12 m

To find x, we apply the trigonometric ratio;

tan Θ = opposite / adjacent -------------------(i)

where Θ = 30°, opposite = x and adjacent = 12m

Substituting these values into equation (i) gives;

=> tan 30° = x / 12

=> 0.5774 = x / 12

Making x the subject of the formula gives;

x = 0.5774 x 12

x = 6.9288 m

x ≅ 6.9m

Therefore the height of the tree is 6.9m

Answer 2

6.93m

Step-by-step explanation:

Using the method of SOH CAH TOA

The base of the tree is 12m which is the adjacent side of the triangle to be generated, the height of the tree will be facing the angle of elevation and it is the opposite side.

Using the formula tan(theta) = Opposite/Adjacent

Given theta = 30°

Adjacent is 12m which is the distance the tree is making with the shadow on the ground

Opposite side will be the height of the tree.

Tan(theta) = height/12

Tan30° = height/12

Height = 12tan30°

Height = 6.93m

Therefore the height of the tree is 6.93m