From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 57°, as shown below. If the distance between the radio antenna and the library is 1.3 miles, how many miles high is the balloon?

I will try my best to answer this, but it will be difficult to determine which angles and distances are where since you did not provide the picture.

You can use the tangent of the 57 degree angle to find your answer.
tan=opposite/adjacent
tan(57 degrees)=1.3/X
X=1.3/tan(57 degrees)

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 2 · 2022-04-27T08:56:17+02:00

The height of the hot air balloon when the distance between the radio antenna and the library is 1.3 miles is 2 miles.

What is right angle triangle property?

In a right angle triangle, the ratio of the opposite side to the adjacent side is equal to the tangent angle between them.

[tex]\tan\theta=\dfrac{b}{a}[/tex]

Here, (a) is the adjacent side, (b) is the opposite side.

From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 57°, as shown below. The distance between the radio antenna and the library is 1.3 miles.

Here, the right angle is made between the height of the balloon (opposite side) and the distance between the radio antenna and the library (adjacent side).

Thus, from the right angle property,

[tex]\tan(57^o)=\dfrac{x}{1.3}\\x=1.3\times\tan(57^o)\\x\approx 2\rm\; mile[/tex]

Thus, the height of the hot air balloon when the distance between the radio antenna and the library is 1.3 miles is 2 miles.

Learn more about the right angle triangle property here;

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