HMWK: p. 554, #s 12 – 25 all Game Plan: Today I will be able to use special right triangles to calculate side lengths. Warm-up: Simplify the following.

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Special Right Triangles

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Presentation transcript:

HMWK: p. 554, #s 12 – 25 all Game Plan: Today I will be able to use special right triangles to calculate side lengths. Warm-up: Simplify the following radicals. Leave in radical form.

Special Right Triangles 45-45-90 Isosceles rt. triangle with angles measures of 45°, 45°, and 90° Ratio of the length of the sides is 1 : 1 : 2 Corresponds to leg : leg : hypotenuse

45-45-90 Example Find the missing length of the side x. leg=x, hyp.=26 2. legs=6, hyp.=x

Special Right Triangles 30-60-90 Rt. triangle with 30°, 60°, 90° angles Ratio of side lengths is 1 : 3 : 2 Corresponds to short leg : long leg : hypotenuse

30-60-90 Examples Find the missing lengths of the sides. 1. 2.

Applications The roof of a doghouse is shaped like an equilateral triangle with height 3 feet. Estimate the area of the cross-section of the roof. Steps Use spec. tri. relationships to find base of triangle Use area formula 3 ft 5.2 ft.

Wrap-Up What do we use the special right triangle relationships to determine? State the 45-45-90 ratio. 30-60-90 ratio. Will begin trig ratios tomorrow – NEED CALCULATORS!!!