SOLUTION: A 30 ft pole casts a shadow as shown in the figure. (a) Express the angle of elevation θ of the sun as a function of the length s of the shadow. θ = (b) Find the a

Algebra ->  Trigonometry-basics -> SOLUTION: A 30 ft pole casts a shadow as shown in the figure. (a) Express the angle of elevation θ of the sun as a function of the length s of the shadow. θ = (b) Find the a      Log On


   

Question 424860: A 30 ft pole casts a shadow as shown in the figure.
(a) Express the angle of elevation θ of the sun as a function of the length s of the shadow.
θ =
(b) Find the angle θ of elevation of the sun when the shadow is 35 ft long. (Round your answer to 4 decimal places.)
rad

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I hope you have the diagram to look at. From the diagram we should be able to tell that the flagpole would be the side "opposite" to angle theta and the shadow would be the "adjacent" side to angle theta.

From our knowledge of the various Trig ratios we should know that the two that involve the opposite and adjacent sides are:
tan = opposite%2Fadjacent
and
cot = adjacent%2Fopposite

So
tan(θ) = 30%2Fs
and
cot(θ) = s%2F30
To express θ, we just use the inverse functions:
θ = tan-1%2830%2Fs%29
or
θ = cot(-1)%28s%2F30%29

To find θ when the shadow is 35 feet long we will use 35 for "s" in one of the equations above and then use our calculators. Since most calculators do not have a button for cot-1 we will use the other equation:
θ = tan-1%2830%2F35%29
The fraction reduces to 5/6:
θ = tan-1%285%2F6%29

Before you start finding the answer, make sure the calculator is set to radian mode. If you do not know how to find or set the mode of your calculator then find
tan(45)
If you get a 1 then you are in degree mode. If not then you are (probably) in radian mode.

If your calculator has buttons for parentheses it is best just to enter what you see on the right side of the equation above. This is so because 5/6 as a decimal is an infinitely long repeating decimal: 0.83333333.... If your calculator does not have buttons for parentheses, then just type in tan-1(0.8333333)). Note: The button for tan-1 can be hard to find. It is often a "shift" or "2nd" button. Be sure not to use tan.

If you were in degree modethen multiply your answer by pi%2F180. You should get a decimal near 0.7. Round this decimal off to the nearest 4 decimal places.