Precal problems featuring triangles

Question

The distance from the tee to the green of a particular golf hole is 290 yd. A golfer hits his drive and paces its distance off at 220 yd. From the point where the ball lies, he measures an angle of 160° between the tee and the green. Find the angle of his drive off the tee measured from the dashed line from the tee to the green shown in the figure. (Round your answer to two decimal places.)

Answer 1

Lauren,

 

You should be able to solve this using the Law of Sines:  sin(a)/A = sin(b)/B = sin(c)/C

 

Let a be the angle at the position of the ball, b be the angle at the green, and c be the angle at the tee.

 

Side A is the distance between the tee and the green and side B is the distance between the ball and the tee.

 

We can solve for angle b since we know angle a, side A and side B

 

sin(b) = B*sin(a)/A = (220)(sin(160°))/(290) = 0.26

 

b = sin ^-1 (0.26) = 15°

 

Finally the sum of the 3 angles of a triangle = 180°, so our answer is (180 -160 -15) = 5°

 

c = 180 -a - b