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Friday, February 5 Essential Questions How do I use inverse sine, cosine, and tangent functions to find the angles of a triangle?

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**5.4 Solve Right Triangles Let be an acute angle.**

Inverse Trigonometric Ratios Let be an acute angle.

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**5.4 Solve Right Triangles Because tan A = _____ = _____ = _____,**

Example 1 Use an inverse tangent to find an angle measure Use a calculator to approximate the measure of to the nearest tenth of a degree. Because tan A = _____ = _____ = _____, Using a calculator, So, the measure of is approximately _______.

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5.4 Solve Right Triangles Checkpoint. Complete the following exercises. In Example 1, use a calculator and an inverse tangent to approximate to the nearest tenth of a degree.

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**5.4 Solve Right Triangles Solution Example 2 sin A = 0.76 cos B = 0.17**

Use an inverse sine and an inverse cosine Let and be acute angles in two right triangles. Use a calculator to approximate the measure of and to the nearest tenth of a degree. sin A = 0.76 Solution cos B = 0.17

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**5.4 Solve Right Triangles Find by using the Triangle Sum Theorem.**

Example 3 Solve a right triangle Solve the right triangle. Round your answer to the nearest tenth. Solution Step 1 Find by using the Triangle Sum Theorem.

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**5.4 Solve Right Triangles Approximate BC using a ______ ratio. sine**

Example 3 Solve a right triangle Solve the right triangle. Round your answer to the nearest tenth. Solution Step 2 Approximate BC using a ______ ratio. sine Write ratio for _________. Multiply each side by ___. Approximate ________. Simplify and round answer.

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**5.4 Solve Right Triangles Approximate AC using a ______ ratio. cosine**

Example 3 Solve a right triangle Solve the right triangle. Round your answer to the nearest tenth. Solution Step 3 Approximate AC using a ______ ratio. cosine Write ratio for _________. Multiply each side by ___. Approximate ________. Simplify and round answer.

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5.4 Solve Right Triangles Example 3 Solve a right triangle Solve the right triangle. Round your answer to the nearest tenth. Solution The angle measures are _____, _____, and _____. The side lengths are _____ feet, about _______ feet, and about ______ feet.

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5.4 Solve Right Triangles Checkpoint. Complete the following exercises. Find to the nearest tenth of a degree if cos T = 0.64. Find to the nearest tenth of a degree if sin D = 0.48.

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5.4 Solve Right Triangles Checkpoint. Complete the following exercises. Solve a right triangle that has a 50o angle and a 15 inch hypotenuse.

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5.4 Solve Right Triangles Pg. 187, 5.4 #1-30

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