Goal 2: To use the properties of 30°-60°-90° triangles Warm-up exercises Solve the equation for the missing variable. Assume all variables are positive. Express the answer in simplified radical form. 1. c 2 = c 2 – 4 2 = a = b 2 = 1296

Solutions

Start with an equilateral, equiangular triangle Draw an angle bisector Isolate one triangle formed. xx 2x2x2x2x 2x2x x To find the third, unknown side of the right triangle, use the Pythagorean Theorem. The Triangle

30 60 x 2x2x b a 2 + b 2 = c 2 Pythagorean Theorem x 2 + b 2 = (2x) 2 Substitution Property of Equality x 2 + b 2 = 4x 2 Simplify b 2 = 3x 2 Subtraction Property of Equality b = Simplify

Theorem: In a triangle, the hypotenuse is twice as long as the shorter leg and the longer leg is times as long as the shorter leg x 2x2x

Short Leg Hypotenuse Long Leg Hypotenuse Long Leg Divide by 2 Divide by Multiply by 2 Multiply by Triangles Always solve for the short leg first.

Ex. Find the values of the variable(s) s 5 t s 30 60

Ex. A tipping platform is a ramp used to unload trucks, as shown in the figure. How high is the end of an 80 foot ramp when it is tipped by a 30 degree angle? by a 45 degree angle?

Ex. The road sign is shaped like an equilateral triangle. Estimate the area of the sign by finding the area of the equilateral triangle.

Assignment Assignment: pp #12-30, 33-39