Question

matt, a six footer, spies a red headed woodpecker on the branch of a tree in his yard. from the ground, the angle of elevation along his line of sight to the bird is 28 degrees. he walks 20 feet towards the tree, and in the same plane as before, now sees the bird at an angle of elevation of 42 degrees. how high in the tree is the bird?

Answer 1

is there a picture for it?

Answer 2

no

Answer 3

tan 28 = x/y + 20 tan 42 = x/y

y + 20 = x/tan 28 y = x/tan 42

y = x/tan 28 - 20 x/tan 28 - 20 = x/ tan 42

tan 42 (x - 20 (tan 28) = x tan 28
x tan 42 - x tan 28 = 20 tan 28
x (tan 42 - tan 28) = 20 tan 28 tan 42

x = 20 tan 28 + tan 42/(tan 42 - tan 28)
x 25.97 + 6 ft.
So 32 ft.