# Unit 7 Part 2 Special Right Triangles 30°, 60,° 90° ∆s 45°, 45,° 90° ∆s.

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Unit 7 Part 2 Special Right Triangles 30°, 60,° 90° ∆s 45°, 45,° 90° ∆s

Special Right Triangles In a 45-45-90 degrees right triangle both legs are congruent and the hypotenuse is the length of the leg times 2 45 1 1

45-45-90 Triangle In a 45-45-90 triangle, the length of the hypotenuse is  2 times the length of one leg. x x x Another way of stating the formula

Example Determine the length of each side of the following 45-45-90 triangle. 5 45 1 1 n w

Find the length of each side. 45 8 √2 8  2 n w 45 1 1

Find the length of each side. The hypotenuse is 6 2 45 6 2 45 1 1 n w

Find the length of each Variable This is a 45-45-90 triangle. x 3 y 45 1 1

30-60-90 triangle In a 30-60-90 right triangle this is the format. 30 60 x2x x 1 1 2 2 Hypotenuse = 2 Adjacent to 30 = Adjacent to 60 = 1

30-60-90 Triangles In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is  3 times the length of the shorter leg. x x  3 2x 30  60  Another way of stating the formula

Example Determine the length of each side of the following 30-60-90 triangle. 16 30 60 1 2 n w

Find the length of each variable. 30 60 y x 5 √ 3 5  3 30 60 1 2

Find the length of each side. 60 30 12 n w 30 60 2 1

Find the length of each variable. 30 60 10 r s 30 60 1 2

30 60 45

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