Trigonometric word problems

Question

A kite has a string length of 14m and forms an angle of 45 degrees with the ground. A gust of wind come along and causes the string to incline at an angle of 60 degree with the ground. What is the change in the height of the kite from the ground. (Include a diagram and answer in an exact value)

Answer 1

Answer:

You are looking for the altitude of the kite above the ground which happens to be the vertical leg of the right angle triangle formed by the 45° angle. If the length of the string is 14 m then sin(45°) = h/14 where is is the vertical leg height, h = 14 sin(45°) = 14(√2/2)= 7√2 m = 9.9 m

When the wind blows and changes the angle to 60° , the string length is is still 14 m and the new height

h1 = 14 sin(60°) = 14( √3/2) = 7√3 = 12.1 m

The difference in height from the ground is ΔH = h1 - h = 12.1 m- 9.9 m = 2.2 m