We will use the tangent trigonometric ratio to solve this problem.
tan(63°) = opposite/adjacent
tan(63°) = 24/x
To solve for x, we can rearrange the equation:
x = 24 / tan(63°)
Calculating the value of x:
x = 24 / tan(63°)
x ≈ 24 / 1.974 = 12.15 miles
Therefore, the balloon is approximately 12.15 miles high.
State the trigonometric ratio you use to solve the following problem, then record your answer.
A right angle is formed by three points: a balloon, an antenna, and a library. The balloon is directly above the antenna, such that the hypotenuse of the triangle is formed by the balloon and the library. The angle with the balloon is labeled 63 degrees, with its opposite side labeled 24 miles and its adjacent side labeled question mark.
From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 63°, as shown below. If the distance between the radio antenna and the library is 24 miles, how many miles high is the balloon? Show your work or explain how you got your answer.
1 answer