Question

A 10-foot tree casts a 17-foot shadow directly down a slope when the angle of elevation of the sun is 42o (see figure). Find \thetaθ, the angle of elevation of the ground (to the nearest tenth of a degree).

Answer 1

The angle of elevation to the nearest degree is 30.5°

To find the angle of elevation , we use trigonometric ratio. Trigonometric ratio is the relationship between the sides of a right triangle.

Sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

where θ is the acute angle.

In this case the angle of elevation is the θ and the height of tree is the opposite and the 17 feet is the adjascent

Tanθ = 10/17

Tanθ = 0.588

θ = 30.5°

The angle of elevation to the nearest degree is 30.5°

Answer 2

The angle of elevation of the ground is 30.5°

Explanation:

Height of the tree=10 foot

length of the shadow=17 foot

we have to determine the angle of elevation of the ground

The tree, shadow and ground forms a right triangle with tree as the height, shadow as the base.

The angle of elevation of the ground θ

tanθ=opposite/adjacent

`=tree length/shadow length\\=10/17\\\\=0.588\\`

θ
`=tan^-1(0.588)=30.5 \°`

The angle of elevation of the ground is 30.5°