Presentation on theme: "What is the area of the triangle? A = 1/2 bh b = cos = x h = sin = y"— Presentation transcript:
1What 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?-11yDo Now:(cos, sin)cosxWhat is the area of the triangle?A = 1/2 bhb = cos = xh = sin = yA = 1/2 (cos)(sin) = 60ºA = 1/2 (cos60)(sin60)
2Un-unit circle is any angle in standard position with (x, y) any point on the terminal side of andr 1yx1-1unit circleHow long is r?
3Model Problem(-3, 4) is a point on the terminal side of . Find the sine, cosine, and tangent of .34r= 5Q II
4Area of Triangle - Angle A C(b cos A, b sin A)(x, y)yhabAcABxbaseArea = 1/2 base · hh = ?base · sin AIf you know the value of c and band the measure of A, thenArea of ∆ABC = 1/2 c • b sinA
5Area of Triangle - Angle B y(c cos B, c sin B)AbhcBaBCxh = ?c sin BIf you know the value of c and aand the measure of B, thenArea of ∆ABC = 1/2 a • c sinB
6Area of Triangle - Angle C By(a cos C, a sin C)achCCbAxh = ?a sin CIf you know the value of a and band the measure of C, thenArea of ∆ABC = 1/2 a • b sinC
7The area of a triangle is equal to one-half Area of TriangleThe area of a triangle is equal to one-halfthe product of the measures of two sidesand the sine of the angle between them.ex. - acute angleFind the area of ∆ABC if c = 8, a = 6, mB = 30ex. - obtuse angleFind the area of ∆BAD if BA = 8, AD = 6, mA = 150
8Find the exact value of the area of an equilateral Model ProblemFind the exact value of the area of an equilateraltriangle if the measure of one side is 4.each side = 4each angle = 60ºABCcab60
9Regents PrepIn ΔABC, mA = 120, b = 10, and c = 18. What is the area of ΔABC to the nearest square inch?
10Find to the nearest hundred the number of Model ProblemFind to the nearest hundred the number ofsquare feet in the area of a triangular lot atthe intersection of two streets if the angle ofintersection is 76º10’ andthe frontage alongthe streets are 220 feetand 156 feet.C156’76º10’220’ABA = 16,700 square feet
11The area of a parallelogram is 20. Find the Model ProblemThe area of a parallelogram is 20. Find themeasures of the angles of the parallelogramif the measures of the two adjacent sides are8 and 5.ABCDA=10Diagonal cuts parallelograminto 2 congruent triangles,each with area of 10.85x180 – xsinA = 1/2mA = 30ºmC = 30ºmB & D = (x – 30º)=150º