pd+01+10

pd 01 10 Problem Ten - Finding the Height of a Tree You have been instructed to measure the tallest tree in a grove. You can't climb to the top of the tree, but you can't see the top of the tree until you move back from it quite a distance. Using an inclinometer, you determine that the angle of elevation to the top of the tree is 28 degrees. Moving 23 feet directly toward the tree on a patch of flat ground, you determine that the angle of elevation to the top of the tree is 42 degrees. Using an altimeter you find that your elevation above sea level is 23 feet while the base of the tree has an elevation above sea level of 218 feet above sea level.

Step one:

Our first step was to sketch the problem with all the information given Our second step was to find the elevation added to the bottom of the tree via information given to the problem Our third step was to find the second angle of the triangle on the right, we were able to do this because of supplementary angles. We also noted the 25 foot height difference Our fourth step was to find a multitude of angles at the top of the triangles. We were able to do this because triangles add up to 180 degrees Our fifth (and only non-sideways step) was to use the law of sines to find the line "x". x is the hypotenuse of the larger triangle. Our sixth step was to use the sine function to find the line "y". Our seventh and final step was to add the y value to the 25 foot elevation difference. Giving us our final answer of the total height of the tree as 54.9.