1)Two buildings are 125 m apart. Standing on the roof of the shorter building, the angle of elevation to the top of the other is 15°. The angle of depression to the base of the other is 25°. How tall are the buildings
2) 7 m long guy wire is attached to the top of a pole. If the base of the wire is attached at a distance of 2 m from the base of the pole. (AP 6)
a) What is the angle of elevation
b) How tall is the pole?
3)A helicopter, flying at an altitude of 750 m, is sighting a landing pad. The angle of depression is 23.4°. How far is the helicopter from the landing pad?
2006-10-17 04:37:05 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
#1. Draw the diagram. You will see that the shorter building (call it b) is the opposite leg of a right triangle with adjacent leg 125 and acute angle 25 degrees. So use tan(25) = b/125.
The taller building is the height of the shorter plus ths opposite leg (t) of a triangle with adjacent leg 125 and angle 15 degrees. So use tan(15) = t/125 and add this to b to get the total height.
2006-10-17 04:53:48 · answer #1 · answered by hayharbr 7 · 0⤊ 0⤋
1.
Short building is 125*tan(25) = 58.29m
Taller building is 125*tan(25)+125*tan(15) = 91.78m
2.
a) acos(2/7) = 73.4 degrees
b) sqrt(7^2 - 2^2) = 6.71m
3.
750/sin(23.4) = 1888.47m Note this is the distance as measured directly from the helicopter to the pad, not the distance as measured along the ground beneath the chopper. From your question it is unclear what distance is needed.
2006-10-17 05:12:57 · answer #2 · answered by 1,1,2,3,3,4, 5,5,6,6,6, 8,8,8,10 6 · 0⤊ 0⤋
Distance between the buidings =125m
1) Lets call the height from the top of thetaller building to the roof level of the shorter building as "X" and the height of the shorter building as "Y". a diagram would be helpful here but I cant draw it here!
X = 125*tan(15) = 125*0.2679 = 33.5 ( to the first approx.)
To get Y use the expression tan(25) = X + Y/125
or
tan(25) = (33.5 + Y)/125
0.4663 = (33.5 + Y)/125
0.4663*125 = 33.5 + Y
58.3 =33.5 + Y
or Y = 58.3 - 33.5 = 24.8m
The height of the taller building is 33.5 + 24.8 = 58.3m
The height of the shorter building is, of course, 24.8m
2) Use sin(theta) = 2/7
theta (the angle of elevation) = arcsin(2/7) = 16.6 degrees
b) tan(16.6) = h/2m
0.2981 = h/2 =0.6m
3) tan(23.4) = 750/S
where S is he horizontal distance to he pad
S = 750/tan(23.4) = 1733m or 1.733km
2006-10-17 06:31:52 · answer #3 · answered by quark_sa 2 · 0⤊ 1⤋
1)
h1 = 125tan25 = 58.288 m
h2 = h1 + 125tan15 = 91.782 m
2)
a) A = arcsin(2/7) = 16.6 deg
b) h = 7 cosA = 6.7082 m
3)
Dh = 750 / tan(23.4) = 1,733.1 m
D = 750 / sin(23.4) = 1,888.5 m
2006-10-17 05:08:04 · answer #4 · answered by Helmut 7 · 0⤊ 1⤋
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2006-10-17 05:04:18 · answer #5 · answered by Anonymous · 0⤊ 1⤋