### Finding angles

To find angles, we can use what are known as inverse trigonometric functions.  On your calculator, the inverse trig functions will appear as $$SI{N^{ - 1}}$$, $$CO{S^{ - 1}}$$, or $$TA{N^{ - 1}}$$. The output of these functions should always be understood as angles.  Use the following procedure to find angles:

1. Compute the sine, cosine, or tangent of the given angle (whichever is most convenient for you).
2. Evaluate the inverse trig function for that number.

Example:  Find the measure of the indicated angle to the nearest degree.

Solution:  Let’s compute the cosine of the angle.  We have

$$\large \cos \left( ? \right) = \frac{{48}}{{52}} \approx 0.923$$

Now we use the inverse cosine button on the calculator to compute

$${\cos ^{ - 1}}0.923 \approx 22.631^\circ$$

We round this result to $$23^\circ$$. Now let’s try one more example:

Example:  Find the measure of the indicated angle to the nearest degree.

Solution:  This time, just to be different, let’s compute the sine of the given angle.  We have

$$\large \sin \left( ? \right) = \frac{{54}}{{90}} = 0.6$$

Since we used sine, we will compute the inverse sine of 0.6. We have

$${\sin ^{ - 1}}0.6 \approx 36.870$$

We round this result to $$37^\circ$$.

15332 x

Find each angle measure to the nearest degree.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Watch bellow how to solve this example:

5504 x

Find the measure of the indicated angle to the nearest degree.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Watch bellow how to solve this example:

7272 x

Find the measure of the indicated angle to the nearest degree.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Watch bellow how to solve this example:

### Geometry

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Congruent Triangles
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Parallel Lines and the Coordinate Plane
Properties of Triangles

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