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306090 TrianglesCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! 306090 trianglesAnother type of special right triangles is the 30° 60° 90° triangle. This is right triangle whose angles are 30°, 60°and 90°. The lengths of the sides of a 30° 60° 90° triangle are in the ratio 1:√3:2 Side1: Side2 : Hypotenuse = a : a√3 : 2a Some Solved Examples Example 1 : Find the length of the hypotenuse, if the two sides are 5√3 and 5. Solution : As the two sides fit in the ratio a : a√3 : 2a a = 5 Hypotenuse = 2a Hypotenuse = 2 x 5 = 10 Example 2 : Find x and y Solution : As the given triangle is a special triangle of 30  60 90. The ratio for this triangle is Side1: Side2 : Hypotenuse = a : a√3 : 2a Here hypotenuse = 2a = 16 So, a = 8 y = 8 x = 8√3 ___________________________________________________________________ 2) In a right triangle, the longest side is 12cm. Find the long leg and short leg. Solution : Longest side= Hypotenuse (H)= 12 cm (side opposite to 90 ^{0} Short leg is the side across 30 ^{0} SL = ½ x H SL = ½ x 12 = 6cm Long leg is the side across 60 ^{0} LL = SL x √3 LL = 6√3 cm __________________________________________________________________ 3)In Δ ABC, AC= 14 cm; BC= 7 cm and AB= 7√3 cm. Find the measures of angles A, B and C. Solution AC = 14cm; BC = 7cm and AB =7√3cm From the above information we can see that, AC = 2 x BC and it is longest side than the other two. So, AC will be the hypotenuse. The angle between AC is B So,∠B = 90 ^{0} BC = 7cm which is the one half of hypotenuse. So, short leg = SL = 7cm ∴ ∠A = 30 ^{0} AB= 7√3cm which is √3 times SL ∴ ∠C = 60 ^{0} Special Right Triangles Special Right Triangles 306090 Triangles Pythagorean Theorem Covid19 has affected physical interactions between people. Don't let it affect your learning.
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