A man looking at a building at a 62 defree angle is standing 12 feet from the base. Find the height of thebuilding to the nearest hundredth of a foot.
2007-08-11 05:18:42 · 10 answers · asked by liz 2 in Science & Mathematics ➔ Mathematics
Draw the picture.
You end up with a right triangle, where the bottom right angle is 62 degrees and the bottom length is 12 feet.
Use your trigonometry.
SOH CAH TOA, which stands for:
Sine: Opposite over Hypotenuse
Cosine: Adjacent over Hypotenuse
Tangent: Opposite over Adjacent
You have an angle and an adjacent side, and you are looking for the opposite side. Use tangent.
tan(62) = x / 12
12tan(62) = x
22.5687 = x
The building is approximately 22.57 feet tall.
2007-08-11 05:30:21 · answer #1 · answered by its_victoria08 6 · 0⤊ 0⤋
The building, the ground, and the line of sight form a right triangle. You can use this equation:
tan(angle) = opposite_leg / adjacent_leg
tan(62) = h / 12
h = 12 * tan(62)
h = 22.569
To the nearest hundredth of a foot, h=22.57. However, that is the height from the man's eyeball to the top of the building. Without knowing the height of the man's eye above the ground (to the nearest hundredth of a foot!), you don't really know the building's height all that accurately. (And even that is assuming, which is not stated in the problem, that the man is looking up at the top of the building, and not some point halfway up the building.)
2007-08-11 05:29:06 · answer #2 · answered by McFate 7 · 2⤊ 0⤋
From that angle, the height of the building is the opposite side of the triangle, the 12 feet is the adjacent side. Tangent is defined as opposite/adjacent.
Tan(62)= 1.8807=h/12
h=12(1.8807)
h=22.57 feet
2007-08-11 05:33:29 · answer #3 · answered by Paladin 7 · 0⤊ 0⤋
Use the rules for right triangles.
One of the angles forms a 68 degree angle, with the opposite side being the unknown height of the building, and the adjacent being the distance from the man to the building. With these two, you can use the tangent function,
tan68 = opposite / adjacent
tan68 = height / 12
height = 12*tan68
height = 29.70 feet
2007-08-11 05:28:27 · answer #4 · answered by Anonymous · 0⤊ 1⤋
/ |
/ |
/ |
/ |
----- --|
the angle of the man is at the bottom left (62 degrees)
The angle of the building is at the bottom right (90 degrees)
the angle at the top is what's left over from the other two (28 degrees) which makes 180 total
the bottom distance is 12 feet.
sin 28 / 12 = sin 68 / x
x = 12sin68 / sin 28
2007-08-11 05:36:49 · answer #5 · answered by Onay 2 · 0⤊ 0⤋
Pythagoras? Triangles. Sin Rules?
90 degrees between the pavement and the building
28 degrees in the other angle. Use the Sin Rule to figure out the other side of the triangle
A / sin A = B/ sin B
A / sin 62 = 12 / sin 28
A = 22.57 ft
maybe?
2007-08-11 05:23:52 · answer #6 · answered by Anonymous · 0⤊ 2⤋
It is like this
Perpendicular/Base =tan 62
or h/12 =tan 62
or h=12 tan 62=22.5687=22.57 ft.
For referance
P/H =sin
B/H=cos
& P/B =tan,P=Perpendicular,H=hypotanuse,&
B=Base
2007-08-11 05:46:49 · answer #7 · answered by MAHAANIM07 4 · 0⤊ 0⤋
if you draw the diagram, you'll see its a right angled triangle, so
tan62 = h/12
1.8807 = h/12
h = 22.57 feet
2007-08-11 05:30:33 · answer #8 · answered by Southpaw 5 · 0⤊ 0⤋
tanθ = y/x
tan62 = y/12
12tan62 = 12(y/12)
12tan62 = y
12(1.880726265) = y
22.56871758 feet = y
22.27 feet. rounded to two decimal places
- - - - - - - s-
2007-08-11 06:24:06 · answer #9 · answered by SAMUEL D 7 · 0⤊ 0⤋
Actually, you need to know the height of the man, as well . . ..
2007-08-11 05:29:27 · answer #10 · answered by Anonymous · 0⤊ 3⤋