HOW TO FIND THE MEASURE OF AN ANGLE USING INVERSE TRIG FUNCTIONS

Find the measure of each angle indicated. Round to the nearest tenth.

Problem 1:

Solution:

tan θ = opposite / adjacent

tan = BC/AC

tan θ = 8/11

θ = tan^-1 (8/11)

θ = 36.02

θ = 36˚

Problem 2 :

Solution :

tan θ = opposite / adjacent

tan θ = AC/BC

tan θ = 13/7

θ = tan^-1 (13/7)

θ = 61.69

θ = 61.7˚

Problem 3 :

Solution :

tan θ = opposite / adjacent

tan θ = BC/AC

tan θ = 11/8

θ = tan^-1 (11/8)

θ = 53.97

θ = 54˚

Problem 4 :

Solution :

   sin θ = opposite / hypotenuse

sin θ = BC/AB

sin θ = 7/9.7

θ = sin^-1 (7/9.7)

θ = 46.19

θ = 46˚

Problem 5 :

Solution :

   cos θ = Adjacent / hypotenuse

cos θ = AC/AB

cos θ = 4/7

θ = cos^-1 (4/7)

θ = 55.15

θ = 55.2˚

Problem 6 :

Solution :

tan θ = opposite / adjacent

tan θ = BC/AC

tan θ = 12/13

θ = tan^-1 (12/13)

θ = 42.70

θ = 42.7˚

Problem 7 :

Solution :

tan θ = opposite / adjacent

tan θ = BC/AC

tan θ = 16/10

θ = tan^-1 (16/10)

θ = 57.99

θ = 58˚

Problem 8 :

Solution :

tan θ = opposite / adjacent

tan θ = BC/AC

tan θ = 5.6/15.3

θ = tan^-1 (5.6/15.3)

θ = 20.10

θ = 20.1˚

Problem 9 :

Solution :

cos θ = Adjacent / hypotenuse

cos θ = AC/AB

cos θ = 9.3/13.2

θ = cos^-1 (9.3/13.2)

θ = 45.20

θ = 45.2˚

Problem 10 :

Solution :

cos θ = Adjacent / hypotenuse

cos θ = AC/AB

cos θ = 2/7

θ = cos^-1 (2/7)

θ = 73.39

θ = 73.4˚