geometry... once again

Question

Find the m .

Answer 1

Remembering our trigonometric functions relationships (SOH-CAH-TOA):

Sin(A) = Opposite side/ Hypotenuse

Cos(A) = Adjacent side/ Hypotenuse

Tan(A) = Opposite side/ Adjacent side

In this figure, with respects to angle A:

Opposite side= 12

Adjacent side= 5

Hypotenuse= 13

Plugging these values in to any of the trigonometric functions:

Sin (A) = 12/13

Therefore:

Sin ^-1(12/13)= A

A=67.38 degrees

If you use any of the other functions, the answer will be the same:

Cos (A) = 5/13

Therefore:

Cos^-1(5/13) = A

A = 67.38 degrees

Tan(A) = 12/5

Therefore:

Tan^-1(12/5)=A

A = 67.38 degrees

***NOTE: Make sure your calculator is in degrees.

Answer 2

sin A = 12 / 13

sin A ≈ 0.923

A ≈ 67.38°