Questions: A right angle is 90° = π/2 radians. If a right triangle has one angle measuring π/2 radians and a second measuring t radians. Find the third angle θ. Give your answer as a mathematical statement that includes the angle t

Solution Steps

To find the third angle \(\theta\) in a right triangle, we need to use the fact that the sum of the angles in any triangle is \(\pi\) radians. Given that one angle is \(\frac{\pi}{2}\) radians and the second angle is \(t\) radians, we can find the third angle by subtracting the sum of the given angles from \(\pi\).

We are given a right triangle with one angle measuring \(\frac{\pi}{2}\) radians and another angle measuring \(t\) radians. We need to find the third angle \(\theta\).

The sum of the angles in any triangle is \(\pi\) radians. For a right triangle, this can be written as: \[ \frac{\pi}{2} + t + \theta = \pi \]

To find \(\theta\), we rearrange the equation: \[ \theta = \pi - \left(\frac{\pi}{2} + t\right) \]

Simplify the right-hand side of the equation: \[ \theta = \pi - \frac{\pi}{2} - t \] \[ \theta = \frac{2\pi}{2} - \frac{\pi}{2} - t \] \[ \theta = \frac{2\pi - \pi}{2} - t \] \[ \theta = \frac{\pi}{2} - t \]

Final Answer