Inverse SOHCAHTOA Way vs Interior Angle Sum
Compare This Method To the tried and true theorem that the sum of the interior angles of a triangle is 180°.
What is the degree measure of LNM?
Since the total measure of the interior angles of a triangle is 180 degrees we can verify the measure of LNM
180° 16°  90° =74 °
Alternately, you could use the inverse of one of the SOHCAHTOA functions, in this case the inverse of sine (sin^{1})! To find, an angle of a right triangle all that we need to know is the length of two sides! Then use the same SOHCAHTOA ratios just in a different fashion See the example below.
YouTube Vid: How to Calculate Inverse SOHCAHTOA
A good video on how to use your a TIGraphing Calculator to calculate the inverse sine,cosine or tangent.
Compare sine with inverse sine.
General Difference: sine is the ratio of two actual sides of a right triangle (the opposite & hypotenuse) sin(B) = AC/ABInverse or sin^{1} is an operation that uses the same two sides of a right triangle as sine does (opposite over hypotenuse) in order to find the measure of the angle (in this case b) sin^{1}(AC/AB) = measure of angle B
Key difference: Although both sine and inverse sine involve the opposite side and hypotenuse of a right triangle, the result of these two operations are very, very different. One operation (sine) finds the ratio of these two sides; the other operation, sine inverse, actually calculates the measure of the angle (B in the example above) using the opposite side and the hypotenuse.
PracticeProblems
Problem 1
Use inverse sine, cosine or tangent to calculate the measure of the shaded angle on the left.
Problem 2
Problem 3
Problem 4
Since you know all 3 sides, you could use any of the following:
= sin^{1}(7/25) = 16.3°= cos^{1}(6/15) = 16.3°
= tan^{1}(7/24) = 16.3°
Problem 5
Since you know all 3 sides, you could use any of the following:
= sin^{1}(8/10) = 53.13°= cos^{1}(6/10) = 53.13°
= tan^{1}(8/6) = 53.13°

Related:
 Sohcahtoa home
 Finding Sine,cosine, tangent ratios
 images
 Inverse Sine Calculator
 Inverse Cosine Calculator
 Inverse Trig Functions worksheet Worksheet with answer key on this page's topicfinding the measure of a right triangle's angle using inverse sine, cosine and tangent