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

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Presentation transcript:

– Use Trig with Right Triangles Unit IV Day 2

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

+ 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.

° ° 30° Special Right Triangles We have two types of special right triangles: and We can find exact side lengths by keeping the radicals in our work.

+ 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

+ 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

+ Example 1 Find the exact values of the variables.

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

+ Example 3 Find the exact values of the variables.

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

+ Example 5 Find the exact values of the variables.

+ Example 6 Find the exact values of the variables.

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