Question

1. choose the correct answer.

image of triangle with vertices c, b, a; cb = 16 mm, ca = 63 mm, ba = 65 mm

a = 16 mm, b = 63 mm, c = 65 mm
the triangle is a(n) ____ triangle.

options: acute, right, obtuse

Explanation:

Step1: Recall Pythagorean theorem

For a triangle with sides \(a\), \(b\), \(c\) (where \(c\) is the longest side), if \(a^{2}+b^{2}=c^{2}\), it is a right triangle.

Step2: Calculate \(a^{2}+b^{2}\)

Given \(a = 16\) mm, \(b=63\) mm, so \(a^{2}=16^{2}=256\), \(b^{2}=63^{2} = 3969\). Then \(a^{2}+b^{2}=256 + 3969=4225\).

Step3: Calculate \(c^{2}\)

Given \(c = 65\) mm, so \(c^{2}=65^{2}=4225\).

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(a^{2}+b^{2}=c^{2}\) (both equal to 4225), by Pythagorean theorem, the triangle is right - angled.

Answer:

right (The triangle is a right triangle because \(16^{2}+63^{2}=65^{2}\) which satisfies the Pythagorean theorem for a right triangle.)