1. + 13.1 – Use Trig with Right Triangles Unit IV Day 2

2. + Do Now Solve for the missing variable. Express your answer as a simplified radical. c 2 = 6 2 + 6 2 a 2 + 8 2 = 16 2

3. + Investigating Special Right Triangles 1. Draw an isosceles right triangle with leg of length 4 or 5 units. Use the Pythagorean theorem to find the length of the hypotenuse. Simplify radicals. 2. Draw an equilateral triangle with side lengths 4, 6, or 8 units. Draw an altitude, creating two congruent right triangles. The length of the short leg must be _____ units. Use the Pythagorean theorem to find the length of the longer leg. Simplify radicals.

4. + 1 1 45° 2 1 60° 30° Special Right Triangles We have two types of special right triangles: 45-45-90 and 30-60-90. We can find exact side lengths by keeping the radicals in our work.

5. + 45°-45°-90° Triangles In a 45°-45°-90° triangle, the hypotenuse is √2 times as long as each leg. x√2 45° Hypotenuse = leg ∙ √2

6. + 30°-60°-90° Triangles In a 30°-60°-90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 times as long as the shorter leg. x√3 60° 30° Hypotenuse =short leg ∙ 2 Long leg = short leg ∙ √3

7. + Example 1 Find the exact values of the variables.

8. + Example 2 Find the value of x. (Is this a special right triangle?) 5 x x

9. + Example 3 Find the exact values of the variables.

10. + 60° Example 4 Find the exact values of the variables.

11. + Example 5 Find the exact values of the variables.

12. + Example 6 Find the exact values of the variables.

13. + Closure What are the two types of special right triangles? What makes each special?