Question

fall 2025 geometry b wwva right triangle relationships and trigonometry use the law of sines to find the value of a. what is the best approximation of the value of a? a 40° 95° 4.7 cm a b c 2.4 cm 3.3 cm 2.7 cm 3.0 cm

Explanation:

Step1: Find angle C

The sum of angles in a triangle is 180°. So, $\angle C=180^{\circ}-40^{\circ}-95^{\circ}=45^{\circ}$.

Step2: Apply 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 $\frac{a}{\sin A}=\frac{b}{\sin B}$, where $b = 4.7$ cm, $A = 40^{\circ}$, and $B=95^{\circ}$. So, $a=\frac{4.7\times\sin40^{\circ}}{\sin95^{\circ}}$.

Step3: Calculate the value of a

$\sin40^{\circ}\approx0.6428$, $\sin95^{\circ}\approx0.9962$. Then $a=\frac{4.7\times0.6428}{0.9962}\approx3.0$ cm.

Answer:

$3.0$ cm