Inverse Trig Functions worksheet Worksheet with answer key on this page's topic--finding the measure of a right triangle's angle using inverse sine, cosine and tangent
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?
Interior Angle Sum Way
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.
Inverse SOHCAHTOA Way
sin-1(73.24/76.19)
=74 °
YouTube Vid: How to Calculate Inverse SOHCAHTOA
A good video on how to use your TI-Graphing Calculator to calculate the inverse sine,cosine or tangent.
Inverse 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.
Practice Problems
Use inverse sine, cosine or tangent to calculate the measure of the shaded angle on the left.
Angle's Measurement
tan-1(24/18) = 53°
Use inverse sine, cosine or tangent to calculate the measure of the shaded angle on the left.
Angle's Measurement
tan-1(5/12) =23°
What is the measure of the shaded angle on the left?
inverse Trig Functions worksheet Worksheet with answer key on this page's topic--finding the measure of a right triangle's angle using inverse sine, cosine and tangent
Inverse Sine Calculator 
Compare sine with inverse sine.
in the triangle below?
Round your answer to the nearest tenth of a degree.
in the triangle below. Round your answer to the nearest hundredth of a degree.
LNM?
180° -16° - 90° =74 ° 
