Question

Quinn is flying a kite. The angle of elevation formed by the kite string and the ground is 40°, and the kite string forms a straight segment that is 100 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.

Answer 1

The distance between the ground and the kite for this case can be known by using trigonometric ratios. This length is deduced to be around 64 ft.

What is angle of elevation?

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

What are the six trigonometric ratios?

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

$\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}$

Consider the diagram attached below.

The length of kite string which is in air  = 100 ft

The angle of elevation from the point of the person flying kite is 40°

Neglecting the height of the person,  we've to find:

The length of side AB, which is the distance between the ground and the kite (perpendicular distance)

The length of side AB is perpendicular from the perspective of angle of elevation, and the hypotenuse' length is known, so we can use either sine or cosecant ratio directly.

Let we use sine ratio. Then, we get:

$\sin(m\angle C) = \dfrac{|AB|}{|AC|}\\\\\sin(40^\circ) = \dfrac{|AB|}{100}\\\\|AB| = 100 \times \sin(40^\circ) \: \rm ft\\\\|AB| \approx 64.28 \: ft \approx 64 \: ft$

Thus, the distance between the ground and the kite for this case can be known by using trigonometric ratios. This length is deduced to be around 64 ft.

Learn more about trigonometric ratios here:

brainly.com/question/22599614

Answer 2

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. sin(θ) = opposite/hypotenusesin(46°) = y/80y = 80sin(46°)plug this in you calculator to get y = 58 feet