Special Right Triangles

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Pythagorean Theorem Properties of Special Right Triangles

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Presentation transcript:

Special Right Triangles Lesson 6-3 Special Right Triangles

30°- 60°- 90° Triangle The sides of a triangle whose angles measure 30°, 60° and 90° have a special relationship. The hypotenuse is always twice as long as the side opposite the 30° angle. c = 2a or a = ½ c 60° 30° a b c Side opposite 30° angle.

Find each missing length. Find the length of side c. Then find the length of side b. 30° 60° b c 6 in a2 + b2 = c2 b2 = c2 – a2 b2 = 122 – 62 b2 = 144 – 36 b2 = 108 b ≈ 10.4 in C = 2a C = 2(6 in) C = 12 in

Find the length of side a. Then find the length of side b. 60° 30° 15 cm a b a2 + b2 = c2 b2 = c2 – a2 b2 = 152 – 7.52 b2 = 225– 56.25 b2 = 168.75 b ≈ 13 cm a = ½c a = ½ (15 cm) a = 7.5 cm

45°-45° Right Triangle c a 45° b Sides a and b are equal. Use Pythagorean to find the missing side. a2 + b2 = c2

Find each missing length. 45° 9 m b c If a = 9, then b = 9 92 + 92 = c2 162 = c2 12.7 m ≈ c

45° c b 18 yd If a = 18, then b = 18 182 + 182 = c2 648= c2 25.5 yd ≈ c