Question

Student lets out 100 feet of string on a kite from a hand height of 3 feet. The angle between horizontal hand height and the kite is 25. Find the height of the kite above the ground, to the nearest foot. Which trig function would be the best function to use for this problem?

Answer 1

Answer: 45.26 ft

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.  

Sin α = opposite side / hypotenuse  

Where α is the angle of elevation of the string to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the string), and the opposite side (x) is the height of the kite above the hand height.

Replacing with the values given:  

Sin 25 = x/ 100  

Solving for x  

sin25 (100) =x  

x= 42.26 ft

Finally, we have to add the hand height:

42.26+3 = 45.26 ft

Feel free to ask for more if needed or if you did not understand something.  

Answer 2

Answer:

Step-by-step explanation:

From the given information, it will make a right triangle, in which hypotenuse =   the length of the string = 100 feet

Let x denote the the height of the kite above the ground.  

By trigonometry,

$\sin25^{\circ}=\frac{\text{side opposite to the angles }}{\text{hypotenuse}}\\\\\Rightarrow\ 0.4226=\frac{x-3}{100}\\\\\Rightarrow\ x-3=42.26\\\\\Rightarrow\ x=42.26+3\\\\\Rightarrow\ x=45.26$

Hence, the height of the kite above the ground = 45.26 feet.

Since the hand is 3 feet above the ground height is ≅ 45