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Volgvan
4 years ago
7

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 th

e ground, it touches the ground a distance of 30 feet from the bottom of the tree. Find the measure of the angle between the kite string and the ground.

Mathematics
2 answers:
weeeeeb [17]4 years ago
8 0

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,

\cos\theta=\frac{\text{Base}}{\text{Hypotenuse}}

\cos\theta=\frac{\text{BC}}{\text{AC}}

\cos\theta=\frac{30}{100}

\cos\theta=0.3

\theta=\cos^{-1}(0.3)

\theta=72.54^\circ

Therefore, The measure of the angle between the kite string and the ground is 72.54°.

spayn [35]4 years ago
6 0
Hyp=100,adj side=30

angle=cos^{-1}(30/100)
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