Chapter 8.3, Problem 43AYU

To determine

How far is the ball from the centre of the green?

Answer to Problem 43AYU

  $\boxed{x\approx 165yards}$

Explanation of Solution

Given information:

A golfer hits an errant tee shot that lands in the rough. A maker in the centre of the fairway is 150 yards from the centre of the green. While standing on the marker and facing the green, the golfer turns $110°$ towards his ball. He then paces off 35 yards to his ball. See the figure. How far is the ball from the centre of the green?

  

Calculation:

Assume the distance between ball and center of the green be $x.$

The distance from marker and the center of the green is 150 yards.

The distance from marker and the ball is 35 yards.

While standing on the marker and facing the green, the golfer turns $110°$ towards the ball so $\theta =110°$ .

The objective is to find thew ball from center of the green.

According to the Law of Cosins, the square of one side of a triangle equals the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of their include angle.

Use the Law of Cosines to find distance between ball and center of the green $x.$

  $x^2={150}^2+{35}^2-\mathrm{2.150.35.}\cos 110°$

  $=22500+1225-\mathrm{2.150.35.}\left(-0.345\right)$

= $22500+1225+3591.2$

=27316.2

Take square roots on the both sides.

  $\sqrt{x^2}=\sqrt{27316.2}$

  $\boxed{x\approx 165yards}$

Hence, the ball from the center of the green is $\boxed{x\approx 165yards}$ .