Angle of Elevation Word Problem Help

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cole92

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A 6-foot person walks from the base of a broadcasting tower directly toward the tip of the shadow cast by the sun. When the person was 132 feet from the tower and 3 feet from the tip of the tower’s shadow, the person’s shadow starts to appear beyond the tower’s shadow.

(A) What is the angle of elevation from the tip of the shadow to the top of the tower? Show your procedure
(B) Find the height of the tower.
(C) Draw the triangle of the tower and its shadow and find all of the sides and angles.
 
Please show whatever work you can accomplish, and try to say something about WHY you're stuck, so that I might determine where to begin helping you.

If there is something about the given information that you do not understand, then ask specific questions.

Part (C) asks you to draw a picture. I would not wait until part (C) to draw a picture. I would start this exercise by drawing a picture. (You can label stuff as you work through the exercise.)

Have you heard of the concept known as "similar triangles"?

This exercise involves two similar right triangles.

People at this site have asked you in the past to SHOW YOUR WORK.

It's time for you to stop posting exercises with no work shown.
 
The furthest I have been able to get is by making a triangle with sides 3, 6, and a hypotenuse of Radical (45). Obviously one angle is 90 degrees, but how do I find the other two?

Since I have my opposite side as 6 and the adjacent as 3, I tried to to acrtan 6/3 in which I got approx. 63.43 degrees as my angle of elevation?
 
cole92 said:
… Obviously one angle is 90 degrees, but how do I find the other two?
Click to expand...


The interior angles of a triangle sum to 180 degrees. Since you've found the angle of elevation, subtract the two known angles from 180 degrees to find the remaining angle.

'
63.43 degrees as my angle of elevation?
Click to expand...


This is correct.

The 3-foot side represents the ground from the tip of the shadow to the person. Extend this side 132 feet from the person to the base of the tower.

Draw a vertical line there to represent the tower.

Extend the hypotenuse from the top of the person to the top of the tower.

You now have a larger right triangle. You know the length of its base. You know all of the angles.

This larger right triangle is similar to the smaller one.

Can you continue?

 
My final answers came out to be a height of 270 ft.

My angles were 90, 63.44 (63), and 26.66 (27)
My sides were 270, 135, and 45 radical 45.

Is this correct?
 
cole92 said:
… My angles were 90, 63.44 (63), and 26.66 (27)

My sides were 270, 135, and 45 radical 45.

Is this correct?
Click to expand...


These results look good to me for part (C), except that the expression 45 sqrt(45) can be simplified because the radicand (45) contains a squared factor (9).

If you're rounding the angles to natural numbers, then you don't need to report the decimal approximations on your diagram. In other words, decide on one format or the other, not both.

 
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