A tower 27.5 meters tall makes an angle of 126 degrees with the inclined road on which it is located. Determine the angle subtended by the tower at a point down the road 35 meters from its foot.
2007-10-31 22:48:54 · 2 answers · asked by delixir_21 1 in Science & Mathematics ➔ Mathematics
that's odd the answer isn't in the multiple choice cause
the multiple choice answers are:
a) 22.5 degrees
b) 23.5 degrees
c) 24.5 degrees
d) 25.5 degrees
2007-11-01 00:50:21 · update #1
give it a quick sketch you have a triangle with 2 sides and an angle.
use cosine rule to find 3rd side (a):
a^2=27.5^2+35^2-2(27.5x35)Cos126
a=55.8m
then sine rule to find angle (B)
55.8/sin126 = 27.5/sinB
B = 54 degrees
2007-10-31 23:24:24 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Let c = distance from the top of the tower to the point on the road.
c^2 = (27.5)^2 + (35)^2 - 2(27.5)(35)cos(126°)
c^2 ≈ 756.25 + 1225 + 1131.487
c^2 ≈ 3112.737
c ≈ 55.79190
Let α = the angle between the road and the top of the tower:
sinα/27.5 ≈ sin(126°)/55.79190
sinα ≈ (27.5)sin(126°)/55.79190
sinα ≈ 0.8090170
α ≈ 54°
2007-10-31 23:31:05 · answer #2 · answered by Helmut 7 · 0⤊ 1⤋