High School

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The angle of elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is 30°. Find the height of the tree.

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A. 39.1 ft

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B. 43.3 ft

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C. 14.4 ft

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D. 17.7 ft

The angle of elevation from a point 25 feet from the base of a tree on level ground to the top of the tree is

Answer :

Hello There!!

Given

[tex] \text{Length of the tree= 25 feet} \\ \text{Angle of Elevation= 30°}[/tex]

To Find

[tex] \text{Height Of The Tree}[/tex]

[tex] \text{Let The Height of the Tree be ‘x’}[/tex]

We Know:-

[tex] \tan\theta = \frac{ \text{perpendicular}}{ \text{base} }[/tex]

[tex] \tan \theta = \frac{ \text{height of the tree}}{ \text{length of the base}} \\ \\ \implies \tan30 = \frac{ \text{x}}{25} \\ \\ \implies \text{x }= 25 \times \tan30 \\ \\ \implies \text{x }= 25 \times 0.577 \\ \\ \implies \text{x} = 14.425 \\ \\ \implies \text{x} = 14.43[/tex]

[tex] \therefore \text{height of the tree(\text{x})} = \red{14.43 \: \text{feet}}[/tex]

Option C is the correct answer

Hope This Helps!!

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Rewritten by : Barada

The answer is C it won’t let me do all the steps but I hope it helps