A communications tower is located at the top of a steep hill, as shown in the figure below. The angle of inclination of the hill is 68°. A guy wire is to be attached to the top of the tower and to the ground, 150 meters downhill from the base of the tower. The angle formed by the guy wire and the hill is 11°. Find the length of the cable required for the guy wire to the nearest whole meter.
I know law of sines but I need Help ASAP!
To find the length of the guy wire, you can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
In this case, we can set up the following proportion:
sin(68°) / x = sin(11°) / (150 + x)
where x represents the length of the guy wire.
To solve for x, we can cross multiply:
sin(68°) * (150 + x) = sin(11°) * x
Now, we can plug in the values and solve for x:
0.92718 * (150 + x) = 0.19081 * x
139.078 + 0.92718x = 0.19081x
0.92718x - 0.19081x = 139.078
0.73637x = 139.078
x = 139.078 / 0.73637
x ≈ 188.922
Therefore, the length of the cable required for the guy wire is approximately 189 meters to the nearest whole meter.
The lost boy: Where are we?
The monster: We are home wherever this is..
but that doesn't matter.
The lost boy: Why not
The monster: Because we have no home
thx scott
the tower should be vertical (90º to the horizontal, and 158º to the side of the hill)
180 - 158 = 22 ... 22 / 2 = 11
so the tower, hillside, and guy wire make a big isosceles triangle
cable length is ... 2 [150 cos(11º)]