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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.

The relative locations of a swing set, a garden, and a sandbox in Gina's backyard-example-1
User Atta
by
8.0k points

2 Answers

7 votes

Answer:

Hello! The correct answer is 34 ft.

Explanation:

I am just confirming!

User Ryan Nigro
by
8.3k points
4 votes

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.

User Nulldroid
by
7.9k points
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