Question

in △klm, k = 50 cm, l = 78 cm and m = 52 cm. find the area of △klm to the nearest 10th of a square centimeter.

Explanation:

Step1: Recall area - formula for triangle

The formula for the area of a triangle given two - side lengths \(k\) and \(l\) and the included - angle \(m\) is \(A=\frac{1}{2}kl\sin m\).

Step2: Substitute the given values

We are given \(k = 50\) cm, \(l=78\) cm, and \(m = 52^{\circ}\). First, find the value of \(\sin(52^{\circ})\). We know that \(\sin(52^{\circ})\approx0.788\). Then substitute \(k = 50\), \(l = 78\), and \(\sin(52^{\circ})\approx0.788\) into the formula \(A=\frac{1}{2}kl\sin m\).

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Step3: Round to the nearest tenth

Rounding \(1536.6\) to the nearest tenth gives \(1536.6\) square centimeters.

Answer:

\(1536.6\) square centimeters