SOLUTION: I'm struggling with this problem. Any help would be appreciated! Here's what I have: A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 8°

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Question 1206614: I'm struggling with this problem. Any help would be appreciated! Here's what I have: A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 8° with the horizontal. The flagpole's shadow is 13 meters long and points directly up the slope. The angle of elevation from the tip of the shadow to the sun is 24°.
Write an equation that you can use to find the height of the flagpole h. It should be something like this:
h/sin ( °) = 13/sin ( °)

Find the height of the flagpole (in m). (Round your answer to one decimal place)
Thank you!

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!






Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
I'm struggling with this problem. Any help would be appreciated! Here's what I have:
A flagpole at a right angle to the horizontal is located on a slope that makes an angle of 8° with the horizontal.
The flagpole's shadow is 13 meters long and points directly up the slope. The angle of elevation from the tip of the shadow to the sun is 24°.
Write an equation that you can use to find the height of the flagpole h. It should be something like this:
h/sin ( °) = 13/sin ( °)
Find the height of the flagpole (in m). (Round your answer to one decimal place)
Thank you!
~~~~~~~~~~~~~~~~~~~~~~~~~~


        You are struggling,  because you did not make very first step.
        This step is to make a plot.
        So,  make a plot and trace my reasoning below.
        I will assume that you have made your plot and it is in front of you.


The acute angle between the flagpole and the slope surface is 90° - 8° = 82°.

The acute angle between the flagpole and the direction to the sun is 90° - 24° = 66°.


It means that the angle of the triangle opposite to the flagpole is  180° - 82° - 66° = 32°.


Now write the sine law in the form, which includes the shadow of 13 m long and the flagpole height h

     = .


From this equation, find h

    h =  =  = 7.540895067.


ANSWER.  The height of the flagpole is about 7.54 meters, or 7 meters and 54 centimeters.

Solved.



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