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Chapter 10: Problem 48

A kite flies at a height of 30 feet when 65 feet of string is out. If the string is in a straight line, find the angle that it makes with the ground. Round to the nearest tenth of a degree.

Short Answer

Expert verified
The angle the string makes with the ground is approximately 24.8 degrees.

Step by step solution

01

Recognize the situation and define the problem.

A right-angled triangle is formed by the height of the kite (30 feet), the length of the string (65 feet), and the ground. The main task is to find the angle that the string (hypotenuse) makes with the ground (adjacent). We are given the length of the opposite side (height of the kite) and the hypotenuse (length of the string).
02

Apply inverse tangent formula.

In trigonometry, the tangent of an angle in a right triangle is the opposite side divided by the adjacent side. We can use the inverse of this function, arctan or tan^-1, to find an angle when we know opposite and adjacent sides. The formula is defined as follows: Angle = tan^-1(Opposite/Hypotenuse). Substituting the given values, we get: Angle = tan^-1(30/65).
03

Calculate the angle

With a calculator, find the arctan of the quotient of the opposite side and adjacent side: tan^-1(30/65) which will give the result in degrees.
04

Round the answer to the nearest tenth of a degree

Finally, since the problem statement asked for the answer to be rounded to the nearest tenth of a degree, ensure to round your response appropriately.

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