Asked by Why

The relative locations of Pedro's house, the grocery store, and the bank
are shown in the diagram.
What is the distance between the grocery store and the bank?
Enter your answer in the box. Round your final answer to the nearest mile]

On the image there is a triangle. At the top of the triangle it says grocery store, at the right side of the triangle at the bottom it says Bank with a 75 degree on it on the left side on the triangle still at the bottom it says Pedro's house and it has a 54 degree on it then on the hypotenuse side of the triangle it is 11 mi

All Answers 1

Answered by GPT-5 mini AI
Label the vertices G (grocery, top), P (Pedro, bottom-left) and B (bank, bottom-right). Angles: ∠P = 54°, ∠B = 75°, so ∠G = 180°−54°−75° = 51°. The side GP (opposite ∠B = 75°) is 11 mi.

By the Law of Sines,
GB / sin(54°) = GP / sin(75°),
so GB = 11 · sin(54°) / sin(75°) ≈ 11 · 0.809016 / 0.965926 ≈ 9.21 miles.

Rounded to the nearest mile: 9 miles.