A elevation word problem

Question

Sarah's cat climed up a tree, that was 10 ft away. If she sees her cat at an angle of elevation of 35° , and her eyes are 5 feet off the ground, how high up from the ground is her cat

Answer 1

A   |\                        We have two right triangles in this problem.  We are given that segment BC is 10', and that angle

     |  \                      ACB is 35^o

     |    \                    So, we can use the tangent function (opposite/adjacent) to figure segment AB

     |     \                   tan 35^o = opp/10' = 0.700 x 10' = 7'

     |      \                  We are given that segment BD = 5' (the height of the observer), which when added to segment AB

     |       \                 gives us 12'

     |        \                Again, we can use the tangent function to calculate segment DE

B   |_____\ C           tan 35^o = 12'/DE; 0.70 x DE = 12'/0.7;  DE = 17.1'

     |          \             We can then use the Pythagorean theorem to solve for segment AE

     |           \            12'² + 17.1'² = AE²; 144'² + 294'² = 438'² = AE²; AE =  20.9'

D   |_______\  E     I am sorry that the spacing didn't work out as I hoped, but I think you will get the idea.