Question

A triangle has an area of 23in^2 and two of the sides of the triangle have lengths 7in. And 8in. Find the sine of the angle theta included by these two sides. (Assume the angle is acute)

Answer 1

sine(θ) ≈ 0.821

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Use the formula for the area of a triangle:

• Area = (1/2) * a * b * sin(θ)

Substitute the given values:

• 23 = (1/2) * 7 * 8 * sin(θ)

Simplify and solve for sin(θ):

• 23 = 28 * sin(θ)
• sin(θ) = 23 / 28
• sin(θ) ≈ 0.821

Hence, the sine of the angle θ included by the two sides is approximately 0.821.