Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. the angle of elevation of the tree from one position on a flat path from the tree is upper h equals 30 degrees commah=30°, and from a second position upper l equals 50 feetl=50 feet farther along this path it is upper b equals 20 degrees .b=20°. what is the height of the tree?

Please find the attached diagram for a better understanding of the solution provided here.

In the attached diagram, OP is the height of the tree.

Rest of the diagram should be sufficiently self explanatory.

In ,

.........................Equation #1

Again, in ,

.........................Equation #2

Thus, equating the equations Equation #1 and Equation #2, we have:

Evaluating we get:

Thus the height of the tree is approximately 49.26 feet

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