Question

select the correct answer.
in a city park, three walking paths form triangle abc. the length ab is 800 meters, the length bc is 900 meters, and the length ac is 850 meters. which angle of this triangle has the greatest measure?
o a. ∠c
o b. cannot be determined
o c. ∠b
o d. ∠a

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger side is opposite the larger angle.

Step2: Compare the side lengths

Given \(AB = 800\) meters, \(BC=900\) meters, \(AC = 850\) meters. We have \(BC>AC>AB\).

Step3: Determine the angle opposite the longest side

The side \(BC\) is the longest side. The angle opposite side \(BC\) is \(\angle A\) (since in \(\triangle ABC\), side \(BC\) is opposite \(\angle A\), side \(AC\) is opposite \(\angle B\), and side \(AB\) is opposite \(\angle C\)).

Answer:

D. \(\angle A\)