Question

A person on a lake sees a plane flying overhead. The angle formed by his line of sight to the plane is 39°; If the plane is flying about 5000 ft, find the horizontal ground distance between the person and the plane.

Answer 1

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$\large \sf \dagger \: {Problem: \dagger}$

A person on a lake sees a plane flying overhead. The angle formed by his line of sight to the plane is 39°; If the plane is flying about 5000 ft, find the horizontal ground distance between the person and the plane.

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$\large \sf \dagger \: {Solution: \dagger}$

• Let x = horizontal ground distance between the person and the plane.

$\qquad\bigstar \: \large \sf{Equation: tan \: 39 \degree = \frac{5000}{x} }$

Solving the equation,

$\large\qquad \implies\tt{tan \: 39\degree = \frac{5000}{x}}$

$\large\qquad \implies \tt{x(tan \: 39 \degree) = \cancel{ x} \large{(} \frac{5000}{ \cancel{x}} \large{)}}$

$\large\qquad\implies \tt \cancel{ \frac{x \: tan \: 39 \degree}{tan \: 39 \degree}} = \frac{5000}{tan \: 39 \degree}$

$\large\qquad \implies \tt{x = \frac{5000}{tan \: 39\degree}}$

$\large \qquad \implies \tt{x \approx \pmb{6174.48758}}$

Checking the solution,

• $\large\tt{tan \: 39 \degree = \frac{5000}{x}}$

• $\large \tt{ tan \: 39 \degree = \frac{5000}{6174.48758}}$

• $\large\tt{0.80978 = 0.80978}$

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$\large \sf \dagger \: {Answer: \dagger}$

• The horizontal distance between the person and the plane is approximately 6174 ft.

$\qquad \rule{200pt}{3pt}$

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