Applying Relationships in Special Right Triangles

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Objective - To use basic trigonometry to solve right triangles.

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Presentation transcript:

Applying Relationships in Special Right Triangles

Special Right Triangle Formulas

The right triangles you explored are sometimes called 45o-45o-90o and 30o-60o-90o triangles. In a 45o-45o-90o triangle, the hypotenuse is √2 times as long as each leg. In a 30o-60o-90o triangle, the hypotenuse is twice as long as the shorter leg and the longer leg is √3 times as long as the shorter leg.

Example 1 Find the unknown side lengths in ΔABC.

Example 2 In right ΔDEF, m ⁄ D :3Oo and m / E = 60o. The shorter leg measures 5√3. Find the remaining side lengths.

Assignments Find the unknown side lengths in each right triangle. 1. 2.

Explain 2 p 712 Trig Ratios of Special Right Triangles A. For each triangle, find the unknown side lengths and trigonometric ratios for the angles. a 45o-45o- 90o triangle with a leg length of I .

Angle sine cosine Tangent

B. A 30o-60o-90o triangle with a shorter leg of I Sine Cosine Tangent 30o 60o

Assignments 1. Find the unknown side lengths and trigonometric ratios for the 45o angle.

Homework Pages 716-717 even # 2 – 12

For each triangle, state whether the side lengths shown are possible For each triangle, state whether the side lengths shown are possible. Explain why or why not. 1. 2.

3. Find the unknown side lengths in each right triangle. 4.

5. Use trigonometric ratios to find the missing lengths and angle.

6.