Question

Anna, Ben, and Cathy are having a treasure hunt. They head off in three different directions to start looking for treasure. After some time, their distances from each other form triangle ABC as shown. Which two friends are farthest apart? a triangle where the measure of angle A, representing Anna, is unknown; angle B, representing Ben, measures 55°; and angle C, representing Cathy, measures 50° A. Anna and Cathy B. Anna and Ben C. Ben and Cathy D. All three are the same distance apart.

Answer 1

Answer: C. Ben and Cathy

Step-by-step explanation:

The diagram showing the triangle ABC is shown in the attached photo.

a represents the distance between Ben and Cathy.

b represents the distance between Andy and Cathy

c represents the distance between Andy and Ben,

The unknown angle A is determined by subtracting the sum of angle B and angle C from 180 degrees. This is because the sum of angles in a triangle is 180 degrees.

Angle A = 180 - (55 + 50)

= 180 - 105 = 75 degrees.

75 degrees is the biggest angle and thus, the farthest distance. It corresponds to a, the distance between Ben and Cathy.