Question

select the correct answer.
marie has a garden in the shape of triangle ( abc ), for which ( mangle a = 51^circ ), ( mangle b = 62^circ ), and ( mangle c = 67^circ ). which side of the garden is the longest?
a. cannot be determined
b. ( overline{ac} )
c. ( overline{ab} )
d. ( overline{bc} )

Explanation:

Step1: Recall the triangle side-angle relationship

In a triangle, the longest side is opposite the largest angle. This is the "largest angle opposite longest side" rule.

Step2: Identify the largest angle

Given angles: \( m\angle A = 51^\circ \), \( m\angle B = 62^\circ \), \( m\angle C = 67^\circ \). Comparing these, \( \angle C \) (67°) is the largest.

Step3: Determine the side opposite \( \angle C \)

In \( \triangle ABC \), the side opposite \( \angle C \) is \( \overline{AB} \). So, \( \overline{AB} \) is the longest side.

Answer:

C. \(\overline{AB}\)