I'm so confused with this math questioni'm terrible at math?
Two buildings are 35m apart. From the top of the shorter building, the
angle of depression to the base of the other is 47° and the angle of
elevation to the top of it is 21°. Find the height of the taller
building.

answers:
alex say: Hint:
draw a diagram
use SOH , CAH or TOA

Mike G say: s = height of the shorter building
h = height of the taller building above the shorter one
s/35 = tan47
s = 37.533 m
h/35 = tan21 = 13.4352
Height of taller building =
37.533+13.4352
= 50.968 m

oldschool say: Let R be a line from the top of the shorter to the base of the taller:
90°  47° = 43°
R = 35/sin43 = 51.32 = 35/cos47
Hs = R*sin47 = 51.32*sin47 = 37.53m height of the short building
Hd = 35*tan21 = 13.44m the amount taller
So the taller building is 37.53+13.44 = 50.97 or about 51m

King Leo say: .
Height of tall building
= 35 tan(21°) + 35 tan(47°)
= 50.97 m
———— —

Captain Matticus, LandPiratesInc say: Draw it out You have a triangle with an altitude of 35 meters. The side opposite of the observer can be broken into 2 segments, a and b. Using the law of sines, we can find their lengths
sin(47) / a = sin(90  47) / 35
sin(47) / a = cos(47) / 35
35 * sin(47) = a * cos(47)
35 * tan(47) = a
sin(21) / b = sin(90  21) / 35
35 * sin(21) = b * cos(21)
35 * tan(21) = b
35 * tan(47) + 35 * tan(21) =>
35 * (tan(47) + tan(21))
Make sure that your calculator is in degree mode
50.968146077103441512111665466154
To 2 sf
51 m

Jim Moor say: First, draw a pic
use SOHCAHTOA since you have right triangles.

L. E. Gant say: Often, it's a matter of envisioning the problem, especially this kind.
So, sketch the givens:
 draw the ground (horizontal line on the page)
 draw a vertical line for the short building (perpendicular to the ground line
 draw a vertical line for the taller building.
 draw a line perpendicular to the taller line to the "top" of the shorter building
 draw a line from the top of the shorter building to the top of the other one
 draw a line to the top of the shorter building to the bottom of the other
Now, put in the numbers that you know:
the ground between the buildings is 35 metres So two lines have this length.
the angle between the line across from the shorter building and the line to the top of the taller building is 21 degrees, and the line to the bottom of the taller building is 47 degrees.
Now use what you know of trigonometry, geometry and algebra.
Let h be the height of the taller building
and x be the height of the shorter building
so tan(21) = (hx)/35
==> hx = 35tan(21)
and tan(47) = x/35
==> x = 35tan(47)
you have two equations:
add them together
and you get:
h = 35tan(21) + 35tan(47) = 35 (tan(21) + tan(47))
look up tan(21) and tan(47) (or use your calculator)
and do the arithmetic
and you have the right answer

BillM say: That is a simple Right Triangle problem. Actually Two Right Triangles.
You solve the Triangle for the smaller one first then that will give you the numbers you need for the larger one.

derfram say: Draw out a picture. Remember that tan() = opposite/adjacent
Tan(47°) = x/35
35 tan(47°) = x
x = 37.53 m << this is the height of the shorter building
tan(21°) = y/35
35 tan(21°) = y
y = 13.44 m << this is how much higher that tall building is over the shorter building
So height of taller building is x + y = 37.53 + 13.44 = 50.97 m
To use the right number of sig figs, height of taller building is 51 meters.

Starrysky say: Draw it out on graph paper. Use trig functions for angles measured from verticals and horizontals

nbsale say: Lots of correct answers, but they seem to complicate a very simple problem. Many fail to include a good picture, which should really be you starting point.
You solve it in two pieces, finding x and y as shown in the picture, then adding the values.
tan21 = x/35
x = 13.435
tan47 = y/35
y = 37.533
x+y = 50.968
