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A water halloon is being launched into the air at a $73^{\circ}$ angle of elevation from the ground. The water balloon reaches a height of $30$ feet directly above your head. How far from you was the water balloon launched?

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Pythagorean theorem

Full solution

Q. A water halloon is being launched into the air at a

73^{\circ}

angle of elevation from the ground. The water balloon reaches a height of

30

feet directly above your head. How far from you was the water balloon launched?

Prompt: question_prompt: How far from you was the water balloon launched?
Identify: Identify the height (opposite side) and angle of elevation to set up for a trigonometric calculation. $\newline$ Height = $30$ feet, Angle = $73$ degrees.
Use Function: Use the tangent function because we have the opposite side and need to find the adjacent side (distance from you). $\newline$ $\tan(73^\circ) = \frac{\text{Opposite}}{\text{Adjacent}}$ .
Plug in Values: Plug in the known values and solve for the adjacent side (distance). $\newline$ $\tan(73^\circ) = \frac{30}{\text{Adjacent}}$ .
Rearrange Equation: Rearrange the equation to solve for the Adjacent side. $\text{Adjacent} = \frac{30}{\tan(73^\circ)}$ .
Calculate Distance: Calculate the distance using a calculator. $\newline$ Adjacent $\approx \frac{30}{3.2709}$ (using $\tan(73^\circ) \approx 3.2709$ ).
Finish Calculation: Finish the calculation. $\newline$ Adjacent $\approx 9.17$ feet.

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