Help with a math question?

Science & Mathematics by Anonymous 2018-06-23 02:42:09

Social Science

4 answers

two equal sides of an isosceles triangle are given to be 3 feet. the angle between the sides is θ. find the area A of the triangle as a function of (θ/2). the answer may include more than one trigonometric function.

Anonymous

area=0.5a*b*sin(t)=0.5*3*3*2*sin(t/2)*co...
Anonymous

A = (9/2)sinθ A = (9/2)2tan(θ/2)/[1+tan^2(θ/2)] = 9tan(θ/2)/[1+tan^2(θ/2)]
Anonymous

Let z = theta/2. The length of the base of the triangle is 2*(3 ft)*sin(z), and the altitude of the triangle is (3 ft)*cos(z). The area is (9 ft^2)*sin(z)*cos(z), or (9 ft^2)*sin(theta/2)*cos(theta/2).
Anonymous

A = (1/2) * a * b * sin(C) C is the angle between sides a and b (1/2) * 3 * 3 * sin(t) => (9/2) * sin(t) => (9/2) * sin(2 * t/2) => (9/2) * 2 * sin(t/2) * cos(t/2) => 9 * sin(t/2) * cos(t/2)