Question

directions: solve the problem at each station. round measures to the nearest degree. identify the answer and find value of x in the triangle 17 84 65

Explanation:

Step1: Find the third - angle

The sum of angles in a triangle is 180°. Let the third angle be $\theta$. So, $\theta=180-(84 + 65)=31^{\circ}$.

Step2: Use the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Here, we have $\frac{x}{\sin84^{\circ}}=\frac{17}{\sin31^{\circ}}$.

Step3: Solve for $x$

Cross - multiply to get $x=\frac{17\sin84^{\circ}}{\sin31^{\circ}}$. Since $\sin84^{\circ}\approx0.9945$ and $\sin31^{\circ}\approx0.5150$, then $x=\frac{17\times0.9945}{0.5150}\approx33$.

Answer:

$x\approx33$