Question

find the area of this triangle. 17 31° 20 ? square units round to the nearest hundredth.

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle when two sides \(a\), \(b\) and the included angle \(\theta\) is \(A=\frac{1}{2}ab\sin\theta\). Here \(a = 20\), \(b=17\), and \(\theta = 31^{\circ}\).

Step2: Substitute the values into the formula

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Since \(\sin(31^{\circ})\approx0.5150\) (using a calculator), then \(A = 10\times17\times0.5150\).

Step3: Calculate the value

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Answer:

\(87.55\)