Mary S. answered • 05/12/15
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Chemistry and Math Tutor
It is helpful to start a problem like this by drawing a picture of the pool in question. Imagine you can look at the entire pool and draw what it looks like then label what you know. In this case you know that the pool is 30 m long (top distance of your pool trapezoid. Label the shallow end 1.3 m and the deep end 4 m. Define the angle of depression by making a dashed line across your pool cross section at the 1.3 m mark (line should be parallel with the top of the pool) and marking the small angle you've just created as your angle of depression. You have now created a 90 degree angle going from the bottom of the pool and across that line. Now we do a little relabeling. The difference between 4 m and 1.3 m is 2.7 m (add this label to your graph). You have now defined the length of the opposite side of your triangle.
Recall your trigonometric functions SOHCAHTOA. Sin is opposite over hypotenuse. Cos is adjacent over hypotenuse. Tangent is opposite over adjacent. Given opposite and adjacent you have a tangent problem! tan x = 2.7/30. Now we solve for x. if you take the arctan of both sides you will determine the angle x. Just remember that you need to put your calculator in the correct mode. If you want the answer in radians, put the calculator in radian mode (0.09 radians). If you want the answer in degrees, put the calculator in degree mode (5 degrees). I've included the possible answers in correct significant figures. If you don't know what that means, don't worry about it.
