Question

A surveyor standing on a hill 27 feet high looks at a building across a river. The surveyor determines that the angle of depression to the base of the building is 24∘56′ and the angle of elevation to the top of the building to be 49∘6′. Calculate the height of the building in feet to two decimal places.

24degrees and 56' (56/60=.93333333)
49 degrees and 6' (6/60=.1)

tan 24.933333= 12/y
y=12/tan24.933333 = 25.81245

25.81245tan49.10 = 29.79870(+12) = 41.7987 = 42 feet

thank you (it says wrong...:()

Answer 1

I need to know how wide the river is.

Answer 2

where did you get the 12?
If the distance from the hill to the building is y, then
tan24.933 = 27/y
y = 58.078 ft
The height h is thus
27 + 58.078 tan49.1 = 94.047 ft

Answer 3

that 12 was a typo.....It was from another example that the teacher showed us... thank you

Answer 4

Unless maybe the base of the building is at 0 altitude
in that case
tan 24.9 = 27/w
w = 58.2 across river to building
then h = 27 + 58.2 tan 49.1
= 27 + 67.2 = 94.2