1Solve the triangle if one exists Round your answers to two

1.Solve the triangle, if one exists. (Round your answers to two decimal places.)

C = 32.9°, b = 3.90, c = 2.54

2.The following diagram shows two ways to play a golf hole. One is to hit the ball down the fairway on your first shot and then hit an approach shot to the green on your second shot. A second way is to hit directly toward the pin. Due to the water hazard, this is a more risky strategy. The distance AB is 163 yards, BC is 148 yards, and angle A is 41.0°. Find the distance AC from the tee directly to the pin. Assume that angle B is an obtuse angle. (Round your answer to two decimal places.)

Solution

C = 32.9

b = 3.90

c = 2.54

applying sine rule

c / sin C = b / sin B

plugging the values we get

2.54 / sin 32.9 = 3.90 / sin B

4.6762 = 3.90 / sin B

B1 = 56.51 ( smaller B value )

B2 = 180 - 56.51 = 123.49 ( larger B value )

2.54 / sin 32.9 = b / sin 123.49

b = 3.899

A1 = 180 -( 56.51 + 32.9 )

A = 90.59

A2= 180 - ( 123.49+ 32.9 ) = 23.61

a / sin A1 = 2.54 / sin 32.9

a = 4.67 (for smaller B value )

a / sin A2 = b/sin B2

a / sin 23.61 = 3.899 / sin 123.49

a=1.872 ( for larger B value )