This is a right triangle problem where $M$ is the right-angle vertex. Given:

• $\angle E = 44.9^\circ$
• $AM = 86.9$ m (one leg)
• $\angle A$ is unknown
• $AE$, $ME$ are unknown

Step 1: Find $\angle A$

Since the sum of the angles in a triangle is $180^\circ$, and we already have a $90^\circ$ and $44.9^\circ$:

$\angle A = 180^\circ - 90^\circ - 44.9^\circ = 45.1^\circ$

Step 2: Find $ME$ using Trigonometry

Using the sine function:

$\sin(44.9^\circ) = \frac{ME}{86.9}$

$ME = 86.9 \times \sin(44.9^\circ)$

$ME \approx 61.4 \text{ m}$

Step 3: Find $AE$ using Trigonometry

Using the cosine function:

$\cos(44.9^\circ) = \frac{AE}{86.9}$

$AE = 86.9 \times \cos(44.9^\circ)$

$AE \approx 60.7 \text{ m}$

Step 4: Find $AM$

Since $AM = 86.9$ m (already given), no calculation is needed.

Would you like me to verify the calculations or explain further? Here are some related questions:

1. How do trigonometric functions apply to right triangles?
2. Can you determine a missing side using the Pythagorean theorem?
3. How do you solve a triangle if it is not a right triangle?
4. What is the sine rule, and when is it used?
5. How does the cosine rule help find unknown angles and sides?

Tip: Always check if the given triangle is a right triangle before choosing the right method to solve it.