The problem provided is a right triangle where:

• $b = 15 \, \text{m}$
• $c = 20 \, \text{m}$
• We are asked to find the value of the angle, presumably the one opposite side $b$, using trigonometry.

We can use the sine function for this, as sine of an angle in a right triangle is defined as:

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

In this case, the opposite side to the angle is $b = 15 \, \text{m}$, and the hypotenuse is $c = 20 \, \text{m}$. Thus,

$\sin(\theta) = \frac{15}{20} = 0.75$

Now, let's calculate the angle by finding the inverse sine of 0.75:

$\theta = \arcsin(0.75)$

I will compute the value of this angle.The angle $\theta$ is approximately $48.59^\circ$.

Since the options provided are rounded, the closest answer is $50^\circ$.

Would you like further details, or do you have any other questions?

Here are five related questions:

1. What is the cosine of this angle?
2. How would you calculate the length of side $a$ (the adjacent side)?
3. If the angle increased to $60^\circ$, what would the new length of side $b$ be?
4. How can we apply the Pythagorean theorem to check the values of the sides?
5. How does the tangent function relate to this triangle's dimensions?

Tip: For right triangles, always remember that the sine of an angle is the ratio of the opposite side to the hypotenuse!