Question

If a triangle ABC has sides measuring 50,42, and 35, is the triangle a right triangle? if it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0

Answer 1

To determine if triangle ABC with sides measuring 50, 42, and 35 is a right triangle, we can use the Pythagorean theorem which states that in a right triangle:

\[ a^2 + b^2 = c^2 \]

where \( c \) is the length of the longest side.

Here, the longest side is 50. We have:

\[
a = 42, \, b = 35, \, c = 50
\]

Now let's check if:

\[
42^2 + 35^2 = 50^2
\]

Calculating each side:

\[
42^2 = 1764
\]
\[
35^2 = 1225
\]
\[
50^2 = 2500
\]

Now summing \( a^2 \) and \( b^2 \):

\[
1764 + 1225 = 2989
\]

This does not equal \( 2500 \):

\[
2989 \neq 2500
\]

Since \( a^2 + b^2 \neq c^2 \), triangle ABC is not a right triangle.

Thus, the answer is:

0