Quinn is flying a kite. The angle of elevation formed by the kite string and the ground is 46°, and the kite string forms a straight segment that is 80 feet long. Explain how to find the distance between the ground and the kite. Include a description of the triangle you drew to help you solve, including the variables and measurements you assigned to each side and angle. Round your answer to the nearest foot.

Step-by-step explanation:

The angle of elevation between kite string and ground is 46°.

String is straight and length of string = 80 ft

Please have a look at the attached image which is a right angled \triangle ABC.

Quinn is at point C.

The \angle C = 46^\circ (angle between string and ground)

The kite is at the point A.

Length of string, AC = 80 ft

We have to find: The distance between ground and kite i.e. Side AB = ?

By the given statement, we can have a right angled \triangle ABC.

Using trigonometric identity for Sine \theta:

sin \theta = \dfrac{Perpendicular}{Hypotenuse}

Here, perpendicular is side AB and Hypotenuse is AC

\theta =46^\circ

AC = 80 ft

AB = ?

Putting the values:

sin 46= \dfrac{AB}{80}\\\Rightarrow AB = 80 \times sin46\\\Rightarrow AB = 80 \times 0.719\\\Rightarrow AB \approx 58\ ft

Hence, distance between ground and kite is \approx 58\ ft

72 feet.

Step-by-step explanation:

The kite string is the hypotenuse ( the longest side) of  a right-angled triangle  formed between the string, the ground and the height of the kite above the ground.

We have the relation:

sin 46 = opposite side / hypotenuse

= height / length of the kite string, so:

sin 46 = h /  80

h = 80 * sin 46

h = 72.14 feet.

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step-by-step explanation: