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**What is the area of the triangle? A = 1/2 bh b = cos = x h = sin = y **

Aim: How do we find the area of a triangle when given two adjacent sides and the included angle? -1 1 y Do Now: (cos, sin) cos x What is the area of the triangle? A = 1/2 bh b = cos = x h = sin = y A = 1/2 (cos)(sin) = 60º A = 1/2 (cos60)(sin60)

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Un-unit circle is any angle in standard position with (x, y) any point on the terminal side of and r 1 y x 1 -1 unit circle How long is r?

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Model Problem (-3, 4) is a point on the terminal side of . Find the sine, cosine, and tangent of . 3 4 r = 5 Q II

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**Area of Triangle - Angle A**

C (b cos A, b sin A) (x, y) y h a b A c A B x base Area = 1/2 base · h h = ? base · sin A If you know the value of c and b and the measure of A, then Area of ∆ABC = 1/2 c • b sinA

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**Area of Triangle - Angle B**

y (c cos B, c sin B) A b h c B a B C x h = ? c sin B If you know the value of c and a and the measure of B, then Area of ∆ABC = 1/2 a • c sinB

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**Area of Triangle - Angle C**

B y (a cos C, a sin C) a c h C C b A x h = ? a sin C If you know the value of a and b and the measure of C, then Area of ∆ABC = 1/2 a • b sinC

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**The area of a triangle is equal to one-half **

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, mB = 30 ex. - obtuse angle Find the area of ∆BAD if BA = 8, AD = 6, mA = 150

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**Find the exact value of the area of an equilateral **

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 c a b 60

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Regents Prep In ΔABC, mA = 120, b = 10, and c = 18. What is the area of ΔABC to the nearest square inch?

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**Find to the nearest hundred the number of **

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. C 156’ 76º10’ 220’ A B A = 16,700 square feet

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**The area of a parallelogram is 20. Find the **

Model Problem 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 A=10 Diagonal cuts parallelogram into 2 congruent triangles, each with area of 10. 8 5 x 180 – x sinA = 1/2 mA = 30º mC = 30º mB & D = (x – 30º)=150º

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The Product Rule

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The Product Rule

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**Dilating the Unit Circle**

y 3 2 (3cos, 3sin) 3 -1 (2cos, 2sin) 2 1 -3 -2 -1 2 3 x -1 Prove that the length of the hypotenuse is equal to the coefficient common to the coordinate points (x,y). -2 -3

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