Question

The relative locations of a swing set, a garden, and a sandbox in Gina's backyard are shown in the diagram.

What is the distance between the sandbox and garden?



Enter your answer as a decimal in the box. Round only your final answer to the nearest foot.

Answer 1

Hello! The correct answer is 34 ft.

Explanation:

I am just confirming!

Answer 2

Let us suppose the distance between the sandbox and garden is x feet.

Apply the sine law in the given triangle, we have

`(x)/(\sin 65^(\circ))=(36)/(\sin 104^(\circ))\\ \\ \text{On coss multiplying, we get}\\ x\sin 104^(\circ)=36\sin 65^(\circ)\\ \\ x=(36\sin 65^(\circ))/(\sin 104^(\circ))\\ \\ x\approx 33.6`

Therefore, in the nearest foot, the distance between the sandbox and garden is 34 foot.