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Finding a Side of a Right Triangle

At a point 200 feet from the base of a building, the angle of elevation to the bottom of a rod is 35 degrees, and the angle of elevation to the top is 53 degrees , as shown below. Find the height x of the Rod alone.





Solution

This problem includes two right triangles. For the smaller triangle use the information that Tan 35 =a/200 to represent the height of the building: a=200 tan 35.

Now, To find the larger right triangle , use the equation tan 53= (a+s)/200

Finding an Angle of Deprssion

A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep end, as shown bellow. Find the angle of depression of the bottom of the pool.

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Solution

Using tangent

Tan A= opp/adj= 2.7/20=.135
the angle of depression is A= arctan .135 which is about 7.69 degrees.




Trigonometry and Bearings