Sadaf is playing golf. From tee off (vertex T) to hole (vertex H) is 190 yards. Her first shot was 160 yards long; however, she didn't shoot straight at the hole, but was 15 degrees off-line, as shown below. Her second shot (taken from where the first shot landed) was straight at the hole, but was only 45 yards long, so landed short of the hole.

How far is it from where her second shot landed to the hold, to the nearest yard?

Question

Sadaf is playing golf. From tee off (vertex T) to hole (vertex H) is 190 yards. Her first shot was 160 yards long; however, she didn't shoot straight at the hole, but was 15 degrees off-line, as shown below. Her second shot (taken from where the first shot landed) was straight at the hole, but was only 45 yards long, so landed short of the hole.

How far is it from where her second shot landed to the hold, to the nearest yard?

dumbcow · Answer

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Use Law of cosines to find x, this is distance to hole after 1st shot
$$x^2 = 190^2 +160^2 - 2(190)(160) \cos 15$$
Final answer is x-45