Question

in $delta tuv$, $u = 370$ cm, $v = 100$ cm and $angle t = 154^{circ}$. find the area of $delta tuv$, to the nearest square centimeter.

Explanation:

Step1: Recall the area formula for a triangle

The area formula for a triangle with two - side lengths \(a\) and \(b\) and the included - angle \(C\) is \(A=\frac{1}{2}ab\sin C\). In \(\triangle TUV\), let \(a = u = 370\) cm, \(b = v = 100\) cm, and \(C=\angle T = 154^{\circ}\).

Step2: Substitute the values into the formula

We know that \(\sin(154^{\circ})\approx0.4384\). Then \(A=\frac{1}{2}\times370\times100\times\sin(154^{\circ})\).
First, calculate \(\frac{1}{2}\times370\times100 = 18500\).
Then, \(A = 18500\times\sin(154^{\circ})\).
Substitute \(\sin(154^{\circ})\approx0.4384\) into the equation: \(A\approx18500\times0.4384\).
\(A\approx8100.4\).

Answer:

8100 cm²