Use the unit circle to find the value of the trigonometric f

Use the unit circle to find the value of the trigonometric function 14) 2Tt 14) tan D)-5 B) C) Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest tenth of 5) 15) a = 3.8 cm, b=19cm A) A = 26.6\", B = 63.4°, c = 4.2 cm C) A-30.00, B = 60.00, c = 5.7 cm B) A = 58.90, B = 31.1°, c = 4.2 cm D) A-63.4°, B-266\", c = 4.2 cm

Solution

1) tan ( 2pi/3)

tan theta = opposite / adjacent

= sqrt 3/2 / -1/2

tan ( 2pi/3) = - sqrt 3

2) a = 3.8 , b = 1.9

applying law of cosines to find c

c = 3.8^2 + 1.9^2 - 2 (3.8)(1.9) cos 90

c = 4.25

applying law of sines to find the angles

3.8 / sin A = 4.25 / sin 90

A = 63.4 degrees

B = 180 - (90 + 63.4)

B = 26.6

option d is correct