Question

solve the triangle.
write each answer as an integer or as a decimal rounded to the nearest tenth.
e =
f =
m∠g =
submit

Explanation:

Step1: Find angle G

The sum of angles in a triangle is 180°. So, $m\angle G=180^{\circ}-26^{\circ}-49^{\circ}$.
$m\angle G = 105^{\circ}$

Step2: Use the Law of Sines to find e

The Law of Sines states that $\frac{e}{\sin E}=\frac{f}{\sin F}=\frac{EF}{\sin G}$. We know $EF = 14$, $E = 26^{\circ}$, $F=49^{\circ}$, $G = 105^{\circ}$. To find e, we have $\frac{e}{\sin26^{\circ}}=\frac{14}{\sin105^{\circ}}$. Then $e=\frac{14\times\sin26^{\circ}}{\sin105^{\circ}}$.
$e=\frac{14\times0.4384}{0.9659}\approx6.3$

Step3: Use the Law of Sines to find f

Using $\frac{f}{\sin49^{\circ}}=\frac{14}{\sin105^{\circ}}$, then $f=\frac{14\times\sin49^{\circ}}{\sin105^{\circ}}$.
$f=\frac{14\times0.7547}{0.9659}\approx10.9$

Answer:

$e = 6.3$
$f = 10.9$
$m\angle G=105$