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Height of a hot air balloon using Law of Sines

0 votes

The angles of elevation of a balloon from two points A and B on level ground are 24.17 degrees and 47.67 degrees respectively. Points A and B are 8.4 miles apart, and the balloon is between the points, in the same vertical plane. Approximate the height of the balloon above the ground.

asked Feb 26, 2013 in TRIGONOMETRY by rockstar Apprentice

1 Answer

+1 vote

In the triangle ADC tanA = opposite/adjacent

Let opposite side = x, AB = AD + BD = 8.4, and angle A = 24.17, angle B = 47.67

The adjacent = 4.2

tanA = opposite/adjacent

tan(24.17) = x/4.2

The trigonometric table in tan(24.17) = 0.4487

0.4481 = x/4.2

Multiply each side by 4.2

(0.4481)(4.2) = x

x = 1.88202

Therefore the height of the balloon above the ground is 1.88 miles.

answered May 18, 2013 by richardson Scholar

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