Sect. 9.4 Special Right Triangles Goal 1 Side Lengths of Special Right Triangles Goal 2 Using Special Right Triangles in Real Life

(Hint): If you have a leg multiply it by to get the length of the hypotenuse. If you know the hypotenuse divide it by to get the length of the leg. Theorem °- 45°- 90° Triangle Theorem In a triangle, the hypotenuse is times as long as a leg. (In this particular triangle the legs are of equal length.) Side Lengths of Special Right Triangles

45º-45º-90º (Isosceles Right Triangle) "Special" Formulas You must remember that these formulas can be used ONLY in a 45º-45º-90º triangle. Side Lengths of Special Right Triangles

Example 1: Find the value of x.

Side Lengths of Special Right Triangles Example 2: x y Find the value of x and y.

Theorem °- 60° - 90° Triangle 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. (Hint): Calculations on this special right triangle all hinge on the SHORT leg. If you have the short leg, then the hypotenuse is 2 times larger. If you have the short leg, then the long leg is times larger. Side Lengths of Special Right Triangles

30º-60º-90º "Special" Formulas H = hypotenuse LL = long leg (across from 60º) SL = short leg (across from 30º) You must remember that these formulas can be used ONLY in a 30º-60º-90º triangle. Side Lengths of Special Right Triangles

Using the formulas: Hypotenuse is given Find x and y. x is the short leg y is the long leg Side Lengths of Special Right Triangles

Find x and y. 6 is the short leg and x is the hypotenuse y is the long leg Side Lengths of Special Right Triangles Using the formulas: Short Leg is given

Find x and y. 8 is the long leg and x is the hypotenuse y is the short leg (Short Leg is the most important to find) Side Lengths of Special Right Triangles Using the formulas: Long Leg is given*

Side Lengths of Special Right Triangles Ratios of lengths of sides of special triangles 30° - 60° - 90° triangle 45° - 45° - 90° triangle

Using Special Right Triangles in Real Life Example 3: Find the value of x and y.

Using Special Right Triangles in Real Life Example 4: Find the value of x and y.

Using Special Right Triangles in Real Life Find the value of x and y. Example 5:

Using Special Right Triangles in Real Life Example 6: A ramp is used to unload trucks. How high is the end of a 50 foot ramp when the angle the ramp forms with the horizontal is 30°? h What if the angle is 45°?

Using Special Right Triangles in Real Life Example 7: The road sign is shaped like an equilateral triangle with a height of 3 feet. Estimate the area of the sign. 3 x

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