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Anvisha [2.4K]
4 years ago
13

A kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. The angle of elevation form

ed by the string and the ground is 40°. Find the length of the string to the nearest foot.
Mathematics
1 answer:
frozen [14]4 years ago
3 0
If you draw a diagram of this, your given values of the resulting triangle give you the sides opposite and adjacent of the angle. The formula that uses these sides is tangent.

The tangent of an angle is equal to the ratio of the opposite side over the other non-hypotenuse side (adjacent).

Therefore;

tan(40)=70/x
0.83909963117=70/x
0.83909963117x=70
x=70/0.83909963117
x=83.4227514823

Where x is the length of the string in feet.
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Answer:

d=28.28

Step-by-step explanation:

To calculate the lenght of the diagonal d across the square, we can assume that the square it is compound of two right triangles. So, we can resolve this exercise using The Pythagorean Theorem.

<em>The Pythagorean theorem</em> states that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the respective lengths of the legs. It is the best-known proposition among those that have their own name in mathematics.

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To find the value of the lenght of the diagonal d across the square, we have:

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Substituting the values

d=\sqrt{(20)^{2} +(20)^{2} }\\d=\sqrt{400+400} =\sqrt{800} \\d=28.284

Round the answer to 2 decimal places

d=28.28

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