Question

the sides of a triangle are 42, 15, and 39. use the pythagorean theorem to determine if the triangle is right, acute, or obtuse.
answer attempt 1 out of x
the triangle is dropdown with right, obtuse, acute because the square of the largest side dropdown the sum of the squares of the other sides.

Explanation:

Step1: Identify largest side

Largest side is 42. So, \( c = 42 \), \( a = 15 \), \( b = 39 \).

Step2: Calculate \( c^2 \), \( a^2 + b^2 \)

\( c^2 = 42^2 = 1764 \)
\( a^2 + b^2 = 15^2 + 39^2 = 225 + 1521 = 1746 \)

Step3: Compare \( c^2 \) and \( a^2 + b^2 \)

Since \( 1764 > 1746 \) (i.e., \( c^2 > a^2 + b^2 \)), the triangle is obtuse (by the converse of Pythagorean theorem for obtuse triangles: if \( c^2 > a^2 + b^2 \), triangle is obtuse).

Answer:

obtuse