Question

If the rays of the sun hit the ground at a 50° angle, what will be the length of the shadow of a 75 ft tree?​

Answer 1

• The height of the tree is 16.78(2dp) feet

Step-by-step explanation:

Let x be the height of the tree. The length of shadow of tree is l=20 feet and elevation of sun is θ=400.

Then, tanθ=xlortan40=x20orx=20tan40=16.78(2dp)feet

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Answer 2

Answer:

62.9 ft (nearest tenth)

Step-by-step explanation:

Use the tan trig ratio to calculate the length of the shadow.

Tan trigonometric ratio

$\sf \tan(\theta)=\dfrac{O}{A}$

where:

• $\theta$ is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

Let x = length of shadow

Given:

• $\theta$ = 50°
• O = 75
• A = x

Substitute the given values into the formula and solve for x:

$\implies \sf \tan(50^{\circ})=\dfrac{75}{x}$

$\implies \sf x=\dfrac{75}{\tan(50^{\circ})}$

$\implies \sf x=62.93247234...$

Therefore, the length of the shadow is 62.9 ft (nearest tenth)