SOLUTION: A ship is coming into a harbor on an unusually high tide. The ship has to pass under the harbor bridge but the captain doesn't know if the ship will fit. he uses a theodolite to me
Algebra ->
Trigonometry-basics
-> SOLUTION: A ship is coming into a harbor on an unusually high tide. The ship has to pass under the harbor bridge but the captain doesn't know if the ship will fit. he uses a theodolite to me
Log On
Question 806729: A ship is coming into a harbor on an unusually high tide. The ship has to pass under the harbor bridge but the captain doesn't know if the ship will fit. he uses a theodolite to measure the angle at an unknown distance from the bridge and then re-measures the angle when he is 300 meters closer. The first angle measured is 2.3 degrees from sea level and the second angle is 3.3 degrees from sea level. If the ships height is 35metres out of the water, will it fit under the bridge. Show all working. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A ship is coming into a harbor on an unusually high tide.
The ship has to pass under the harbor bridge but the captain doesn't know if the ship will fit.
he uses a theodolite to measure the angle at an unknown distance from the bridge and then re-measures the angle when he is 300 meters closer.
The first angle measured is 2.3 degrees from sea level and the second angle is 3.3 degrees from sea level.
If the ships height is 35metres out of the water, will it fit under the bridge.
:
Draw this out and note the triangle formed
Angle A = 2.3 degrees
Angle B: 180 - 3.3 = 176.7 degrees
Angle C: 180 - 176.7 -2 .3 = 1 degree
:
Using the law of sines, find b, the slant range from the original position of
the ship to the bridge = =
.017452b = 300 * .057564
b =
b = 989.5 meter ship to the bridge
This is the hypotenuse of a right triangle with:
Side opposite Angle A is the vertical height (a) of the bridge
sin(2.3) =
a = sin(2.3) * 989.5
a = 39.7 meters, should just make it
