Question

the angle of elevation from the tip of the shadow to the top of the tree is 36 degrees. find the distance from the top of the tree to the tip of the shadow. round the answer to the nearest tenth.

Answer 1

In order to fully understand the problem, it is best to sketch it. Sketching the system, we will see that the system forms a triangle where the angle of elevation is 36 degrees. We are asked to find the hypotenuse. We can use a trigonometric function. It should be noted that one of the sides should also be given in order to calculate the hypotenuse. Trigonometric functions that can be used are:

sin(theta) = opposite / hypotenuse
cos(theta) = adjacent / hypotenuse

Answer 2

The distance from the top of the tree to the shadow is 40.8 ft.

From the given figure:

cos theta = adjacent/hypotenuse
cos 36= 33/H 
H=33/cos 6= 40.8 ft