Sitting on a park bench, you see a swing that is 100 feet away and a slide that is 60 feet away. the angle between them is 30°. what is the approximate distance between the swing and the slide? a. 120 feet b. 57 feet c. 53 feet d. 147 feet

A.  120 feet

Explanation:

Let A = the location of the slide and B = the location of the swing.  C = your location.

The angle between A and B, ∠CBA, is 30°.

The way I have this set up has the 30° angle across from the 60 ft side.  Using the Law of Sines to solve for ∠BAC,

Cross-multiplying gives us

100(sin 30) = 60(sin A)

Divide both sides by 60:

(100(sin 30))/60 = (60(sin A))/60

0.833333 = sin A

5/6 = sin A

To find the measure of angle A, take the inverse sine:

sin⁻¹(5/6) = A

56.4 = A

This gives us two of the three angles; this leaves the third angle, ∠BCA, to be

180-(30+56.4) = 180-86.4 = 93.6

Using the Law of Sines to find side AB, we have

Cross multiplying, we have

b(sin 30) = 60(sin 93.6)

Divide both sides by sin 30:

(b(sin 30))/(sin 30) = (60(sin 93.6))/(sin 30)

b = 119.76 ≈ 120

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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