Question

a golfer hits her ball a distance of 127 m so that it finishes 31 m from the hole, calculate the angle between the line of her shot and direct line to the shot

Answer 1

Answer on Question #75064, Math / Trigonometry

A golfer hits her ball a distance of $127\mathrm{m}$ so that it finishes $31\mathrm{m}$ from the hole. If the length of the hole is $150\mathrm{m}$, calculate the angle between the line of her shot and direct line to the shot.

Solution

Consider the triangle $\Delta GBH$

$$GH = 150, BH = 31, GB = 127, \angle BGH = \alpha$$

The Law of Cosines

$$(BH)^2 = (GH)^2 + (GB)^2 - 2(GH)(GB) \cos(\angle BGH)$$

Substitute

$$(31)^2 = (150)^2 + (127)^2 - 2(150)(127) \cos \alpha$$

Solve for $\alpha$

$$\begin{array}{l} \cos \alpha = \dfrac{22500 + 16129 - 961}{38100} = \dfrac{3139}{3175} \\ \alpha = \arccos\left(\dfrac{3139}{3175}\right) \approx 8{}^\circ 38' \end{array}$$

Answer: $\approx 8{}^\circ 38'$.

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