We are given the following information about a right triangle:

• $a = 15$ (one side of the triangle),
• Angle $C = 1.5707$ radians (which is very close to $\frac{\pi}{2}$, implying this is the right angle),
• Angle $A = \frac{2n}{15}$ (we'll interpret this expression as $A = \frac{2n}{15}$ radians, where $n$ is an unknown constant).

Step 1: Interpret the angles

Since angle $C$ is a right angle, we know:

• $C = 1.5707$ radians (right angle, $\frac{\pi}{2}$),
• The sum of the angles in any triangle is $180^\circ$ or $\pi$ radians, so: $A + B + C = \pi$ Substituting $C = \frac{\pi}{2}$: $A + B + \frac{\pi}{2} = \pi$ $A + B = \frac{\pi}{2}$

So, angle $B$ is related to angle $A$ as: $B = \frac{\pi}{2} - A$

Step 2: Solve for side $b$ using trigonometry

To find side $b$, we can use the sine or cosine rule. Let's first use the sine rule since we know angle $A$ and side $a$.

• From the sine rule: $\frac{a}{\sin A} = \frac{b}{\sin B}$ Since $B = \frac{\pi}{2} - A$, we have: $\sin B = \cos A$ Substituting this into the sine rule: $\frac{a}{\sin A} = \frac{b}{\cos A}$ Solving for $b$: $b = \frac{a \cos A}{\sin A}$ Substituting $a = 15$: $b = 15 \cdot \frac{\cos A}{\sin A} = 15 \cot A$

Step 3: Solve for angle $A$

We have $A = \frac{2n}{15}$, so we can substitute this expression into the equation for $b$: $b = 15 \cot \left( \frac{2n}{15} \right)$

Step 4: Solve for side $c$

We can find side $c$ using the Pythagorean theorem: $c^2 = a^2 + b^2$ Substitute $a = 15$ and $b = 15 \cot \left( \frac{2n}{15} \right)$: $c^2 = 15^2 + \left( 15 \cot \left( \frac{2n}{15} \right) \right)^2$ $c = \sqrt{15^2 + \left( 15 \cot \left( \frac{2n}{15} \right) \right)^2}$

Conclusion:

To summarize:

• Side $b = 15 \cot \left( \frac{2n}{15} \right)$,
• Angle $B = \frac{\pi}{2} - \frac{2n}{15}$,
• Side $c = \sqrt{15^2 + \left( 15 \cot \left( \frac{2n}{15} \right) \right)^2}$.

If you have a specific value for $n$, we can calculate numerical values for $b$ and $c$.

Would you like to proceed with a specific value for $n$? Or would you like more details?