ss_7_1

# ss_7_1 - Section 7.1 Solving Right Triangles This sections...

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Section 7.1 Solving Right Triangles This sections gives examples that show how to solve for various parts of right triangles, given suﬃcient information about the triangle. Pythagorean Theorem: A triangle with sides a , b , c is a right triangle iﬀ c 2 = a 2 + b 2 . Example. If b =4, α =10 o in the above triangle, ﬁnd a , c , β . Solution. tan α = a b a = b tan α =4tan10 o . 7053 c 2 = a 2 + b 2 = . 7053 2 +4 2 =16 . 497 c =4 . 06 α + β =90 o implies β =90 o - α =90 o - 10 o =80 o Example. Let c = 10, α =40 o in the above triangle. Find b , a , β . Solution. Since α =40 o , β =90 o - 40 o =50 o . sin β = b c = b 10 implies b =10sin β =10s in50 o =7 . 66 cos β = a c = a 10 implies a =10cos β = 10 cos50 o =6 . 43. Example. One angle of a right triangle is π 8 radians and one leg is 3 meters. Find the length of the hypotenuse c . Solution. Case 1. The side adjacent to the π 8 angle is 3.

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ss_7_1 - Section 7.1 Solving Right Triangles This sections...

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