Question

solve the right triangle.

m = 30.7° (round to one decimal place as needed.)
n = 209 m (round to the nearest integer as needed.)
p = 243 m (round to the nearest integer as needed.)

right triangle details: right angle at p, side pn = 124 m, angle at n = 59.3°, side pm = n, side mn = p, angle at m = m

Explanation:

Step1: Calculate angle M

In a right triangle, the sum of acute angles is $90^\circ$.
$M = 90^\circ - 59.3^\circ = 30.7^\circ$

Step2: Calculate side $n$

Use tangent of $\angle N$: $\tan(N)=\frac{n}{PN}$
$n = 124 \times \tan(59.3^\circ) \approx 124 \times 1.685 = 209$

Step3: Calculate side $p$

Use cosine of $\angle N$: $\cos(N)=\frac{PN}{p}$
$p = \frac{124}{\cos(59.3^\circ)} \approx \frac{124}{0.510} = 243$

Answer:

$M = 30.7^\circ$
$n = 209$ m
$p = 243$ m