Question

1. choose the correct answer.

image of triangle with vertices c, b, a; sides: 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: right, obtuse, acute

Explanation:

Step1: Recall Pythagorean theorem

For a triangle with sides \(a\), \(b\), \(c\) (where \(c\) is the longest side), check if \(a^2 + b^2 = c^2\) (right), \(a^2 + b^2 < c^2\) (obtuse), or \(a^2 + b^2 > c^2\) (acute). Here, \(a = 16\), \(b = 63\), \(c = 65\) (longest).

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

\(a^2 = 16^2 = 256\), \(b^2 = 63^2 = 3969\). Sum: \(256 + 3969 = 4225\).

Step3: Calculate \(c^2\)

\(c^2 = 65^2 = 4225\).

Step4: Compare

Since \(a^2 + b^2 = c^2\), the triangle is right.

Answer:

A. right