Question

A tree that is 10 yards tall and casts a shadow 14 yards long. find the angle of elevation from the tip of the shadow to the top of the tree. Round to the nearest degree

-54 degrees
- 36 degrees
- 46 degrees
- 44 degrees

Answer 1

The correct answer is 36 degrees.

Answer 2

36 degrees

Explanation:

Refer the attached figure .

Height of tree i.e. AB = 10 yards

Length of shadow i.e. BC = 14 yards .

We are required to find the angle of elevation from the tip of the shadow to the top of the tree. i.e. ∠ACB

Now, we will use trigonometric ratio.

`tan\theta = (Perpendicular)/(Base)`

`tan\theta = (AB)/(BC)`

`tan\theta = (10)/(14)`

`tan\theta =0.714`

`\theta =tani^(-1)0.714`

`\theta =35.52^(\circ)`

Thus the angle of elevation is 35.52° ≈ 36°

Hence the angle of elevation from the tip of the shadow o the top of the tree. i.e. ∠ACB is 36°