# A famous golfer tees off on a straight 390 yard par 4 and slices his drive to the right. The drive goes 280 yards from the tee. Using a​ 7-iron on his second​ shot, he hits the ball 180 yards and it lands inches from the hole. How many degrees​ (to the nearest​ degree) to the right of the line from the tee to the hole did he slice his​ drive?

## To find the number of degrees to the right of the line from the tee to the hole that the drive was sliced, we need to calculate the angle formed by the tee, the ball's landing spot, and the hole.

First, let's find the distance between the tee and the ball's landing spot. Since the golfer sliced his drive to the right, we need to subtract the distance the ball traveled from the total distance of the hole:

Total distance of the par 4 hole = 390 yards
Distance the ball traveled = 280 yards
Distance between the tee and the ball's landing spot = Total distance - Distance traveled
= 390 yards - 280 yards
= 110 yards

Next, we need to calculate the distance between the tee and the hole. Since it is a straight par 4, we can assume the golfer hit the ball directly towards the hole (ignoring the slice):

Distance between the tee and the hole = 390 yards

Now, we can use the trigonometric function "tan" to calculate the angle to the right of the line from the tee to the hole:

In this case, the opposite side is the distance between the tee and the ball's landing spot (110 yards), and the adjacent side is the distance between the tee and the hole (390 yards).

= tan^(-1)(110/390)

Calculating this using a calculator, we find that:

angle ≈ 16.8 degrees

Therefore, the golfer sliced his drive approximately 16.8 degrees to the right of the line from the tee to the hole.

## To find the number of degrees the golfer sliced his drive to the right of the line from the tee to the hole, we can use trigonometry.

First, let's calculate the distance from the tee to where the ball should have landed if it did not slice. We know the golfer hit a 280-yard drive and the hole is 390 yards away. So, the remaining distance the ball should have traveled is 390 - 280 = 110 yards.

Now, let's calculate the angle the golfer sliced the ball. We can use the sine of this angle to find the ratio of the distance sliced to the total distance that the ball should have traveled.

sin(angle) = distance sliced / total distance

In this case, the distance sliced is 280 yards (the distance the ball actually traveled) and the total distance should have been 110 yards (the straight line distance from the tee to where it should have landed).

sin(angle) = 280 / 110

Now, let's calculate the angle using the arcsin function on a calculator:

angle = arcsin(280 / 110)

The result is approximately 68.19 degrees.

Therefore, the golfer sliced his drive approximately 68 degrees to the right of the line from the tee to the hole.

## Instead of the triangle having sides 390, 280, and 180

let's use the similar triangle of 39, 28, 18 , the angles of course remain the same.

looks like we need the angle opposite the side 18,
using the cosine law:
18^2 = 39^2 + 28^2 - 2(39)(28) cosØ
2184cosØ = 1981
cosØ = 1981/2184 = ....

Ø =