Derive the triangle area formula A=1/2ab sin(C) using an auxiliary altitude.
Find a triangle’s area from two sides and the included angle by expressing the altitude with sine
Problem
\(\text{Two}~\text{property}~\text{boundaries}\) are \(80~m\) and \(120~m\) long and meet at \(65°\), as shown. Write a trigonometric expression for the enclosed triangular area with units.
Use either property boundary as the base and convert the other boundary into perpendicular height with the sine of their included angle. Substituting that height into one-half base times height yields one-half the product of both boundaries and the sine factor. Keep the exact trigonometric expression and attach square units unless a decimal is requested.
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