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Colton is flying a kite, holding his hands a distance of 3 feet above the ground and letting all the kite's string play out. He measures the angle of elevation from his hand to the kite to be 32°. If the string from the kite to his hand is 90 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
90
32°
13
3
The kite is feet above the ground.

Colton is flying a kite holding his hands a distance of 3 feet above the ground and letting all the kites string play out He measures the angle of elevation fro class=

Respuesta :

roohafzah

Answer :

  • 50.69 ft

Explanation :

first let us find the value of x using the law of sines

  • sinX/x = sinY/y

here,

X = 32°

x = ?

Y = 90°

y = 90 ft

plug in,

x = sin(32°)*90ft/sin(90°)

  • x = 47.69 ft

thus, the kite is 47.69 ft + 3 ft = 50.69 ft above the ground.

semsee45

Answer:

50.69 ft

Step-by-step explanation:

To find the height of the kite above the ground, we can use the sine trigonometric ratio to find the value of x, then add this to the distance Carlton's hands are from the ground.

[tex]\boxed{\begin{array}{l}\underline{\textsf{Sine trigonometric ratio}}\\\\\sf \sin(\theta)=\dfrac{O}{H}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$\theta$ is the angle.}\\\phantom{ww}\bullet\;\textsf{O is the side opposite the angle.}\\\phantom{ww}\bullet\;\textsf{H is the hypotenuse (the side opposite the right angle).}\end{array}}[/tex]

In this case:

  • θ = 32°
  • O = x
  • H = 90

Substitute the values into the sine ratio and solve for x:

[tex]\sin 32^{\circ}=\dfrac{x}{90}\\\\\\x=90\sin 32^{\circ}\\\\\\x=47.69273378...\\\\\\x=47.69\; \sf ft[/tex]

Since Colton is holding his hands a distance of 3 feet above the ground, we need to add 3 to the value of x to find the height the kite is above the ground:

[tex]\textsf{Height}=x+3\\\\\\\textsf{Height}=47.69+3\\\\\\\textsf{Height}=50.69\; \sf ft[/tex]

Therefore, the kite is 50.69 ft above the ground.

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