Answer:
The measure of the angle between the kite string and the ground is 72.54°.
Step-by-step explanation:
Given : A kite with a 100 foot-long string is caught in a tree. When the full length of the string is stretched in a straight line to the ground, it touches the ground a distance of 30 feet from the bottom of the tree.
To find : The measure of the angle between the kite string and the ground.
Solution :
Refer the attached figure.
In a right angle ΔABC,
A kite with a 100 foot-long string is caught in a tree.
i.e, AC=100 ft.
Length of the string touches the ground a distance of 30 feet from the bottom of the tree.
i.e, BC=30 ft.
We have to find the angle C between the kite string and the ground.
Apply trigonometric function,
[tex]\cos\theta=\frac{\text{Base}}{\text{Hypotenuse}}[/tex]
[tex]\cos\theta=\frac{\text{BC}}{\text{AC}}[/tex]
[tex]\cos\theta=\frac{30}{100}[/tex]
[tex]\cos\theta=0.3[/tex]
[tex]\theta=\cos^{-1}(0.3)[/tex]
[tex]\theta=72.54^\circ[/tex]
Therefore, The measure of the angle between the kite string and the ground is 72.54°.
