Question

question. in △uvw, u = 5 cm, ∠w = 25° and ∠u = 19°. find the area of △uvw, to the nearest 10th of a square centimeter. answer. attempt 1 out of 2 score: 4/5 penalty: none show examples watch video submit answer

Explanation:

Step1: Recall the area - formula for a triangle

The area formula for a triangle given two - angles and the included side is $A=\frac{1}{2}u^{2}\frac{\sin V\sin W}{\sin U}$. First, find angle $V$. Since the sum of angles in a triangle is $180^{\circ}$, $V = 180^{\circ}-(U + W)$. Given $U = 19^{\circ}$ and $W=25^{\circ}$, then $V=180-(19 + 25)=136^{\circ}$.

Step2: Substitute values into the formula

We know $u = 5$ cm, $\sin U=\sin19^{\circ}\approx0.326$, $\sin V=\sin136^{\circ}\approx0.695$, $\sin W=\sin25^{\circ}\approx0.423$. Substitute into $A=\frac{1}{2}u^{2}\frac{\sin V\sin W}{\sin U}$. So $A=\frac{1}{2}\times5^{2}\times\frac{0.695\times0.423}{0.326}$.

Step3: Calculate the area

First, calculate the numerator of the fraction: $0.695\times0.423 = 0.294$. Then, $\frac{0.294}{0.326}\approx0.902$. Next, $\frac{1}{2}\times25\times0.902 = 11.275\approx11.3$ square centimeters.

Answer:

$11.3$