Question

find the area of the triangle having the given measurements.

b = 49°, a = 7 yards, c = 10 yards

a≈ square yards (round the answer to the nearest square unit.)

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle when two sides \(a\), \(c\) and the included angle \(B\) are known is \(A=\frac{1}{2}ac\sin B\).

Step2: Substitute the given values into the formula

Given \(a = 7\), \(c=10\), and \(B = 49^{\circ}\). First, find \(\sin(49^{\circ})\). Using a calculator, \(\sin(49^{\circ})\approx0.7547\). Then substitute into the formula: \(A=\frac{1}{2}(7)(10)(0.7547)\).

Step3: Calculate the value of \(A\)

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Answer:

\(26\) square yards