APPLICATIONS As our study of trigonometry progresses we will

APPLICATIONS As our study of trigonometry progresses, we will learn to find the measure of an angle based on its trig function values (first studied in Section 2.2). Here we practice finding these trig function values. 83. Billiards: In Carolina\'s attempt to end a pool game by sinking the eight ball, she \"scratches,\" accidentally sending the cue ball into the corner pocket located 60 in. to the west and 40 in. to the north of where it contacted the eight ball. Find tan , for the angle shown. For convenience, a coordinate system is shown with the point of contact at the origin. 40 60 84. Ice hockey: Wydonyu Yustrig takes a low slap shot from the blue line, as shown in the figure.

Solution

83)

from the figure we have

tan ( 180 - theta ) = 40/60

- tan theta = 40/60

tan theta = -2/3

theta = 146.31 degrees

85) length of the brush is 10 inches

which is the hypotenuse of the triangle

now she raises the brush to 3 inches

this is now the perpendicular of the trangle

so , now finding sin theta

sin theta = perpendicular / hypotenuse

sin theta = 3 / 10

theta = sin^-1 (3/10) = 17.46 degrees

87) the ball travels 70 ft through the air which is hypotenuse of triangle

now the point of contact is 60ft

so horizontal distance = 60ft

applying cos rule

cos theta = base / hypotenuse

cos theta = 60/70

cos theta = 6/7

theta = 31 degrees