Question

6. A golfer is standing at the tee,
looking up to the green on a hill. If the
tee is 36 yards lower than the green
and the angle of elevation from the tee
to the hole is 12º, find the distance from
the tee to the hole.​

Answer 1

Answer:

173.15 yards is the distance from tee to hole.

Step-by-step explanation:

Please refer to the image attached.

Let A is the position of tee and where the golfer is standing.

C is the position of hole.

CB is the vertical distance between greens and tee.

Angle of elevation, $\angle BAC = 12^\circ$

To find: side AC.

Using trigonometric functions, we know that value of sine is:

$sin\theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}$

Here $\theta = \angle BAC = 12^\circ$

Perpendicular is side CB.

Hypotenuse is side AC.

$sin12^\circ = \dfrac{\text{CB}}{\text{AC}}\\\Rightarrow \text{CB} = \dfrac{36}{sin12^\circ}\\\Rightarrow \text{CB} = 173.15\ yards$

Hence, 173.15 yards is the distance from tee to hole.