To solve this right triangle problem, we can follow the given steps. Let's break it down:

Step 1: Triangle Information

• The triangle $\triangle NMP$ is a right triangle.
• We are given:
  • Angle $\angle M = 40.1^\circ$
  • Angle $\angle N = 49.9^\circ$
  • Hypotenuse $NP = 121$ m.

We need to find the lengths of sides $n$ (adjacent to $\angle N$) and $p$ (opposite $\angle N$).

Step 2: Use Trigonometric Functions

Finding side $n$ (adjacent to $\angle N$):

We can use the cosine function for this: $\cos(49.9^\circ) = \frac{n}{121}$ Solving for $n$: $n = 121 \times \cos(49.9^\circ)$

Finding side $p$ (opposite $\angle N$):

We can use the sine function for this: $\sin(49.9^\circ) = \frac{p}{121}$ Solving for $p$: $p = 121 \times \sin(49.9^\circ)$

Now, let's calculate the values of $n$ and $p$.The calculations give us the following results:

• The length of side $n$ (adjacent to $\angle N$) is approximately 78 meters.
• The length of side $p$ (opposite $\angle N$) is approximately 93 meters.

Would you like more details on how these values were derived, or do you have any other questions?

Here are some related questions:

1. How can we verify these results using the Pythagorean theorem?
2. What trigonometric function is used to find the hypotenuse given two sides?
3. How do different angles affect the side lengths in a right triangle?
4. What are the other possible ways to solve a right triangle?
5. What is the significance of rounding in practical triangle problems?

Tip: When working with angles and trigonometric functions, always ensure your calculator is in the correct mode (degrees or radians).