Question

Marie has a garden in the shape of triangle ABC, for which m∠A=51∘, m∠B=62∘. Which side of the garden is the longest?

A) Side AB
B) Side BC
C) Side AC

Answer 1

To find the longest side of triangle ABC given two angles (m∠A=51°, m∠B=62°), calculate the third angle (m∠C) and determine that the longest side is opposite the largest angle, which is side AB.

Step-by-step explanation:

The longest side of a triangle is always opposite the largest angle. In this case, we know two angles of the triangle: m∠A=51° and m∠B=62°. To find the largest angle, we first need to calculate the third angle of the triangle. Since the sum of the angles in a triangle is 180°, we can find the third angle m∠C.

m∠C = 180° - m∠A - m∠B

m∠C = 180° - 51° - 62°

m∠C = 67°

Since 67° is the largest angle, the longest side will be opposite this angle, which is side AB.