Question

One angle of a triangle is 74°74\degree74° . How many degrees must one of the other angles be for the Pythagorean Theorem to be true for the triangle?

Answer 1

The Pythagorean Theorem applies specifically to right triangles, where one of the angles must be \(90^\circ\). In a triangle, the sum of all angles is always \(180^\circ\).

Given one angle is \(74^\circ\), we denote the other two angles as \(B\) and \(C\). To find the constraints for one of these angles to create a right triangle, we can set:

\[
B = 90^\circ
\]

Now, we can find \(C\):

\[
74^\circ + 90^\circ + C = 180^\circ
\]

This simplifies to:

\[
164^\circ + C = 180^\circ
\]

Subtracting \(164^\circ\) from both sides gives:

\[
C = 180^\circ - 164^\circ = 16^\circ
\]

Thus, for the triangle to satisfy the Pythagorean Theorem, one of the other angles must be \(90^\circ\), and the remaining angle will be \(16^\circ\). Therefore, the answer is:

**One of the other angles must be \(90^\circ\).**