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There are two special types of right triangles: There are two special types of right triangles: 30 60 90 Triangles 60 30 There are two special types of right triangles: 30 60 90 Triangles 60 30 45 45 90 Triangles 45 45 30 What angles goes here? 45 What angle goes here? 30 45 45 Each of these triangles have their own specific pattern 30 60 Each of these triangles have their own specific pattern The angle across from the 90∘ angle equals 2 30 60 Each of these triangles have their own specific pattern The angle across from the 90∘ angle equals 2 30 2 60 Each of these triangles have their own specific pattern The angle across from the 60∘ angle equals √3 30 2 √3 60 Each of these triangles have their own specific pattern The angle across from the 30∘ angle equals 1 30 2 √3 60 1 Match the sides 30 2 ? √3 ? 60 1 ? A 45-45-90 triangle also has its own unique pattern A 45-45-90 triangle also has its own unique pattern 45 45 A 45-45-90 triangle also has its own unique pattern √2 is opposite of the 90∘ angle 45 45 A 45-45-90 triangle also has its own unique pattern √2 is opposite of the 90∘ angle 45 √2 45 A 45-45-90 triangle also has its own unique pattern And 1 is opposite both 45∘ angles 45 √2 45 A 45-45-90 triangle also has its own unique pattern And x is opposite both 45∘ angles 45 √2 1 45 1 Match the sides 45 √2 ? 1 45 1 ? To solve for one of the sides of a 30-60-90 triangle you first have to be able to find opposite sides To solve for one of the sides of a 30-60-90 triangle you first have to be able to find opposite sides 30 c a 60 b doesn't touch the angle An opposite side is the side that To solve for one of the sides of a 30-60-90 triangle you first have to be able to find opposite sides Side c 30 c a 60 b doesn't touch the angle An opposite side is the side that To solve for one of the sides of a 30-60-90 triangle Side c you first have to be able to find opposite sides Side c 30 c a 60 b doesn't touch the angle An opposite side is the side that To solve for one of the sides of a 30-60-90 triangle Side c you first have to be able to find opposite sides Side c doesn't touch the 90∘ angle 30 c a 60 b doesn't touch the angle An opposite side is the side that To solve for one of the sides of a 30-60-90 triangle Side c you first have to be able to find opposite sides Side c doesn't touch the 90∘ angle 30 c a 60 b doesn't touch the angle An opposite side 90∘ angle is the side that To solve for one of the sides of a 30-60-90 triangle Side c you first have to be able to find opposite sides Side c doesn't touch the 90∘ angle so side c is OPPOSITE the 90∘ angle 30 c a 60 b doesn't touch the angle An opposite side 90∘ angle is the side that 30 c a 60 b Likewise, Side a Side a 30 c a 60 b Likewise, Side a Side a 30 c a 60 b Likewise, Side a is opposite the 60∘ angle Side a 30 60∘ angle c a 60 b Likewise, Side a is opposite the 60∘ angle 30 Which side is opposite the 30∘ angle? c a 60 b side a side b side c side d 30 Which angle is side c opposite from? c a 60 b 30∘ 60∘ 90∘ 45∘ In order to use 30-60-90 triangles In order to use 30-60-90 triangles you must be able to match the triangle you are given In order to use 30-60-90 triangles you must be able to match the triangle you are given 60∘ 8 x 30∘ y In order to use 30-60-90 triangles you must be able to match the triangle you are given 60∘ 8 with the formula triangle x 30∘ y In order to use 30-60-90 triangles you must be able to match the triangle you are given 60∘ 8 with the formula triangle x 30∘ y 2 60∘ 1 30∘ √3 In order to use 30-60-90 triangles you must be able to match the triangle you are given (2) 60∘ 8 with the formula triangle x 30∘ y 2 60∘ 1 30∘ √3 In order to use 30-60-90 triangles you must be able to match the triangle you are given (2) 60∘ 8 with the formula triangle x (1) 30∘ y 2 60∘ 1 30∘ √3 In order to use 30-60-90 triangles you must be able to match the triangle you are given (2) 60∘ 8 with the formula triangle x (1) 30∘ y (√3) 2 60∘ 1 30∘ √3 60∘ (2) ? (1) ? 30∘ (√3) ? 2 60∘ 1 30∘ √3 (1) ? 60∘ (√3) ? (2) ? 2 60∘ 1 30∘ √3 30∘ Then set up a proportion (2) 60∘ 8 x (1) 30∘ y (√3) 2 60∘ 1 30∘ √3 Then set up a proportion (2) 60∘ 8 x (1) 30∘ y (√3) 2 60∘ 1 30∘ √3 Then set up a proportion (2) 60∘ 8 x (1) 30∘ y (√3) 2 8 = 2 60∘ 1 30∘ √3 parenthesis Then set up a proportion on top (2) 60∘ 8 x (1) 30∘ y (√3) 2 8 = 2 60∘ 1 30∘ √3 Then set up a proportion (2) 60∘ 8 x (1) 30∘ y (√3) 2 8 = 2 60∘ 1 30∘ √3 Then set up a proportion (2) 60∘ 8 x (1) 30∘ y (√3) 2 8 = 2 60∘ 1 x 1 30∘ √3 parenthesis Then set up a proportion on top (2) 60∘ 8 x (1) 30∘ y (√3) 2 8 = 2 60∘ 1 x 1 30∘ √3 Then solve the proportion (2) 60∘ 8 x (1) 30∘ y (√3) 2 8 = 2 60∘ 1 x 1 30∘ √3 Then solve the proportion (2) 60∘ 8 x (1) 30∘ y (√3) 2 8 = 2 60∘ 1 x 1 30∘ √3 2x = 8 Then solve the proportion (2) 60∘ 8 x (1) 30∘ y (√3) 2 8 = 2 60∘ 1 x 1 30∘ √3 2x = 8 x = Put parenthesis on top 7 ? 2 ? = 1 ? x 7 60ο (2) (1) x 30ο ( 3 ) Cross Multiply Put parenthesis on top 7 2 = 2 ? x = 1 x 7 ? 7 60ο (2) (1) x 30ο ( 3 ) Cross Multiply Put parenthesis on top Solve 7 2 = 2 x = x = 1 x 7 7 60ο (2) (1) x 30ο ( 3 ) |