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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Aim: How do we find the area of a triangle when given two adjacent sides and the included angle? Do Now: y x (cos, sin ) What is the area of the triangle? cos A = 1/2 bh A = 1/2 (cos )(sin ) b = cos = xh = sin = y = 60º A = 1/2 (cos60)(sin60)

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Un-unit circle is any angle in standard position with (x, y) any point on the terminal side of and y x unit circle r 1

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Model Problem (-3, 4) is a point on the terminal side of. Find the sine, cosine, and tangent of. r = Q II

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Area of Triangle - Angle A y x (b cos A, b sin A) b a h c AB C Area of ABC = 1/2 c b sinA h = ?base · sin A If you know the value of c and b and the measure of A, then Area = 1/2 base · h A (x, y) base

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Area of Triangle - Angle B y x (c cos B, c sin B) c b a h A C B Area of ABC = 1/2 a c sinB h = ? c sin B If you know the value of c and a and the measure of B, then B

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Area of Triangle - Angle C y x (a cos C, a sin C) c a b h B A C Area of ABC = 1/2 a b sinC h = ?a sin C If you know the value of a and b and the measure of C, then C

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Area of Triangle The area of a triangle is equal to one-half the product of the measures of two sides and the sine of the angle between them. ex. - acute angle Find the area of ABC if c = 8, a = 6, m B = 30 ex. - obtuse angle Find the area of BAD if BA = 8, AD = 6, m A = 150

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Model Problem Find the exact value of the area of an equilateral triangle if the measure of one side is 4. each side = 4 each angle = 60º A B C ca b 60

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Regents Prep In ΔABC, m A = 120, b = 10, and c = 18. What is the area of ΔABC to the nearest square inch?

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Model Problem Find to the nearest hundred the number of square feet in the area of a triangular lot at the intersection of two streets if the angle of intersection is 76º10 and the frontage along the streets are 220 feet and 156 feet. A B C º10 A = 16,700 square feet

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. The area of a parallelogram is 20. Find the measures of the angles of the parallelogram if the measures of the two adjacent sides are 8 and 5. A B C D Model Problem x – x Diagonal cuts parallelogram into 2 congruent triangles, each with area of 10. sinA = 1/2 m A = 30º A=10 m C = 30ºm B & D = (x – 30º)=150º

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. The Product Rule

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. The Product Rule

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Aim: Finding Area of Triangle Course: Alg. 2 & Trig. Dilating the Unit Circle y x (2cos, 2sin ) (3cos, 3sin ) Prove that the length of the hypotenuse is equal to the coefficient common to the coordinate points (x,y).

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