Question

law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ in $\triangle bcd$, $d = 3$, $b = 5$, and $mangle d=25^{circ}$. what are the possible approximate measures of angle b? only $155^{circ}$ $45^{circ}$ and $135^{circ}$

Explanation:

Step1: Apply the law of sines

According to the law of sines $\frac{\sin B}{b}=\frac{\sin D}{d}$. Substitute $d = 3$, $b = 5$, and $m\angle D=25^{\circ}$ into the formula. We get $\sin B=\frac{b\sin D}{d}=\frac{5\sin25^{\circ}}{3}$.

Step2: Calculate $\sin B$

We know that $\sin25^{\circ}\approx0.4226$, so $\sin B=\frac{5\times0.4226}{3}=\frac{2.113}{3}\approx0.7043$.

Step3: Find the possible values of angle B

Since $\sin B\approx0.7043$, and the sine - function has a value of $y = 0.7043$ for two angles in the range $0^{\circ}

Answer:

45° and 135°