Question

solve the right triangle.

write your answers as integers or as decimals rounded to the nearest tenth.
$ef = $
$eg = $
$m\angle f = \quad ^\circ$

Explanation:

Step1: Calculate $\angle F$

Sum of triangle angles is $180^\circ$.
$m\angle F = 180^\circ - 90^\circ - 59^\circ = 31^\circ$

Step2: Find length $EG$

Use cosine of $\angle G$.
$\cos(59^\circ) = \frac{EG}{FG} \implies EG = FG \cdot \cos(59^\circ) = 7 \cdot \cos(59^\circ) \approx 7 \cdot 0.5150 = 3.6$

Step3: Find length $EF$

Use sine of $\angle G$.
$\sin(59^\circ) = \frac{EF}{FG} \implies EF = FG \cdot \sin(59^\circ) = 7 \cdot \sin(59^\circ) \approx 7 \cdot 0.8572 = 6.0$

Answer:

$EF = 6.0$
$EG = 3.6$
$m\angle F = 31^\circ$