Kendra is flying a kite 35 feet in the air. The angle of depression from the kite to where Kendra holds the string is 32 degrees. If Kendra holds the string 3 feet off the ground, what is the distance from her hands to the kite? Round your answer to the nearest tenth.
Height of the kite from the hand
=35-3 = 32 ft
Distance of the kite from hand
= x feet
using the formula
sin(32) =32/x
x = 32/sin(32) =60.3865572736188208=60.4 .............Ans(c)
To find the distance from Kendra's hands to the kite, we can use trigonometry and the angle of depression.
Let's denote the distance from Kendra's hands to the kite as "x".
Since we are given the angle of depression as 32 degrees, we can use tangent to find the value of "x".
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the kite from the ground (35 feet - 3 feet) = 32 feet, and the adjacent side is the distance from Kendra's hands to the kite (x).
Thus, we have the equation:
tan(32) = opposite side / adjacent side
tan(32) = 32 / x
To solve for x, we rearrange the equation:
x = 32 / tan(32)
Calculating this expression gives us:
x ≈ 57.4 feet
Therefore, the distance from Kendra's hands to the kite is approximately 57.4 feet.
To find the distance from Kendra's hands to the kite, we can use trigonometry and the concept of angles of elevation and depression.
Let's visualize the problem. We have a right triangle where:
- The vertical leg represents the height of the kite (35 feet).
- The horizontal leg represents the distance from Kendra's hands to the kite.
- The angle of depression is the angle between the horizontal leg and the line of sight from the kite to Kendra's hands (32 degrees).
Since we know the height of the kite and the angle of depression, we can use the tangent function.
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the kite, and the adjacent side is the horizontal distance from Kendra's hands to the kite.
So, we have the following equation:
tan(32 degrees) = opposite side / adjacent side
Plugging in the known values:
tan(32 degrees) = 35 / x
where x represents the distance from Kendra's hands to the kite.
To solve for x, we rearrange the equation:
x = 35 / tan(32 degrees)
Using a calculator, we find:
x ≈ 60.96 feet
Therefore, the distance from Kendra's hands to the kite is approximately 60.96 feet.