Question

1 fill in the blank 1 point what is the area of the triangle? round your answer to the nearest tenth. area = type your answer... square units

Explanation:

Step1: Recall the formula for the area of a triangle with two sides and included angle

The formula for the area of a triangle when two sides \(a\) and \(b\) and the included angle \(C\) is \(A=\frac{1}{2}ab\sin C\). Here, \(a = 14\), \(b=19\), and \(C = 56^{\circ}\).

Step2: Substitute the values into the formula

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Since \(\sin(56^{\circ})\approx0.829\) (using a calculator), then \(A = 133\times0.829\).

Step3: Calculate the value

\(A=133\times0.829 = 110.257\approx110.3\)

Answer:

\(110.3\)