Area of Triangles C a b A B c

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Area = ½ bc sinA = ½ ab sinC = ½ ac sinB

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Presentation transcript:

Area of Triangles C a b A B c Area = 1/2bc sinA or Area = 1/2ac sinB or Area = 1/2ab sinC : To use this formula, you must know 2 sides & the angle between them (the angle formed by the 2 sides).

C b a A B 3.58 Ex: Find the area of the triangle to the nearest tenth. 1. C : To use this formula, you must know either a or b…this means we must use law of sines or law of cosines to find the missing sides. We can find a or b…it doesn’t matter. b =3.5 73˚ a 37˚40’ 69˚20’ A B 3.58 : We found C by taking 180-(sum of A+B). Area = 1/2bc sinA Area = 3.8 sq. units

C 12 5 A B 13 Ex: Find the area of the triangle to the nearest tenth. 2. C : We need to use the Law of Cosines to find one of the angles…it doesn’t matter which one. You may notice that 5, 12, & 13 are pythagorean triples which means this is a right triangle…C=90˚ 90˚ 12 5 A B 13 : We’ll pretend we didn’t know it was a right triangle. Area = 1/2ab sinC Area = 30 sq. units

A 15 20 C B a Ex: Find the area of the triangle to the nearest tenth. 3. A : We know 2 sides & the angle between them, so we can simply use the area of a triangle formula. 115˚ 15 20 C B a Area = 1/2bc sinA Area = 135.9 sq. units

Ex: Find the area of each circular segment to the nearest tenth, given its central angle Ø, and the radius of the circle. 4. : All radii of a circle are equal…this means we know 2 sides of a triangle & the angle between them. Area of Area of circular segment = Area of sector “Plan of Attack”: Area of circular segment = Area of sector - Area of Area = 1/2bc sinA A =1/2 (7)(7)sin(π⁄8) A = 9.376 Area of sector=πr2•[(π/8)/2π] A=π•49•.0625 A≈9.621 Area of circular segment = 9.621 - 9.376 A≈.245 or .2 (to nearest tenth)