Trigonometry Worksheets (Missing Sides)

In these free math worksheets, students learn to find missing sides of a right triangle using Trigonometry.

There are two sets of Find Missing Sides worksheets:
Find missing sides of triangles
Missing sides word problems

How to find missing sides using Trigonometry?

To find missing side lengths using trigonometry when given a side and an angle in a right triangle, we can follow these steps:

1. Identify the known side and angle:
   Label the sides of the triangle as opposite, adjacent, and hypotenuse in reference to the given angle. Mark the known side length and angle on the diagram.
2. Choose the appropriate trigonometric ratio:
   Use the acronym SOH CAH TOA to determine which trigonometric ratio to use based on the known and missing sides:
   SOH: Sine = Opposite/ Hypotenuse
   CAH: Cosine = Adjacent/ Hypotenuse
   TOA: Tangent = Opposite/ Adjacent
3. Set up the equation and solve:
   Substitute the known values into the chosen trigonometric ratio. Solve for the missing side length using algebraic manipulation.

Here are some examples:

Example 1:
Given a right triangle with a hypotenuse of 10 cm and an angle of 30°, find the length of the side opposite the angle.

Solution:
Known side: Hypotenuse = 10 cm
Known angle: 30°
Needed side: Opposite
Trigonometric ratio: SOH (because we are looking for the opposite side)
Equation: sin(30°) = Opposite / 10
Solve: Opposite = 10 * sin(30°) = 5 cm

Example 2:
Given a right triangle with an adjacent side of 6 cm and an angle of 45°, find the length of the hypotenuse.

Solution:
Known side: Adjacent = 6 cm
Known angle: 45°
Needed side: Hypotenuse
Trigonometric ratio: CAH (because we are looking for the hypotenuse)
Equation: cos(45°) = 6 / Hypotenuse
Solve: Hypotenuse = 6 / cos(45°) = 8.49 cm

Click on the following worksheet to get a printable pdf document.
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