Question

A flagpole casts a 40-foot shadow. The angle of elevation from the tip of the
shadow to the tip of the flagpole is 34. How tall is the flagpole? Round your
answer to the nearest foot.
A. 29 feet
B. 22 feet
C. 27 feet
D. 33 feet

Answer 1

Answer:

27 Feet is the answer. Option C.

Answer 2

The flagpole is 27 feet tall.

What is right triangle?

"It is a triangle whose one of the angle measures 90° "

What is tangent of angle?

For angle $\theta$, $tan(\theta)=\frac{opposite ~side~of~angle~\theta}{adjecent~side~of~angle~\theta}$

What is angle of elevation?

"An angle that is formed between the horizontal line and the line of sight. "

For given question,

Consider the following diagram.

Here, AB = the flagpole,

A flagpole casts a 40-foot shadow.

so, BC = 40 foot

The angle of elevation from the tip of the shadow to the tip of the flagpole is 34°.

⇒ ∠ACB = 34°

We need to find the height of the flagpole.

We find the tan of angle 34°

$\Rightarrow tan(34)=\frac{AB}{BC}\\\\ \Rightarrow 0.6745=\frac{AB}{40}\\\\\Rightarrow AB=0.6745\times 40\\\\\Rightarrow AB = 26.98\\\\\Rightarrow AB\approx 27~feet$

Therefore, the flagpole is 27 feet tall.

Learn more about the tan of angle here:

https://brainly.com/question/14347166

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