Solving For Unknown Angles And Sides Using Trigonometric Ratios
Label each of the sides on the following right triangles as
Hypotenuse, Opposite, or Adjacent with respect to the marked reference angle.
1.5 cm
B
A
3.81 cm
4.02 cm
3.27 cm
2.24 cm
1.74 cm
3.59 cm
C
3.39 cm
3.34 cm
Write the three primary trig ratios for each of the reference angles in these triangles.
sin A 
 0. _______
sin B 
 0. _______
cos A 
 0. _______
cos B 
 0. _______
tan A 
 0. _______
tan B 
 0. _______
Find the measurements of each of the angles in the triangles above. Show your work.
Verify that your answer is correct by checking it with each of the ratios.
For the right triangle shown:
49
3.8 cm
1. Label each of the sides as Hypotenuse, Opposite, or Adjacent
2. How could you use one of the trig ratios (sin, cos, or tan) to solve for the
length of side a?
a
Solving for an unknown angle
You have to know two sides
Solving for an unknown side
If you know two sides
If you only know one side and
one angle
1. Determine which sides are
known (H, O, A)
1. Identify the hypotenuse
1. Determine which sides are
known (H, O, A)
2. Set up a trig ratio involving
the unknown angle and the
known sides
2. Set up Pythagorean theorem
with the hypotenuse isolated
on one side of the equation.
2. Set up a trig ratio involving
the unknown angle and the
known sides
3. Use the inverse ratio (sin-1,
cos-1, or tan-1) to solve
3. Rearrange the equation to
solve for the unknown
3. Solve for the unknown side