suppose that we are standing on a bridge 30 feet above a river watching a log (piece of wood) floating toward we. If the angle with the horizontal to the front of the log is 16.7 degree and angle with horizontal to the back of the log is 14 degree, how long is the log?
if the front of the log is x feet from the bridge, and y is the length of the log, then
30/x = tan 16.7°
30/(x+y) = tan 14°
eliminate x:
30/tan 16.7° = 30/tan 14° - y
Now solve for y:
y = 30(cot 14° - cot 16.7°)
Good
Aisha
To find the length of the log, we can use trigonometry. Let's call the length of the log "L".
Since we are standing on a bridge and the angles with the horizontal are given, we can use the tangent function to relate the height of the bridge and the length of the log.
First, let's calculate the height difference between the front and the back of the log.
Height difference (h) = tan(angle with the back of the log) * Length of the log (L)
= tan(14°) * L
Similarly, the height difference between the front of the log and the river's surface is:
Height difference (h) = tan(angle with the front of the log) * Distance to the log from the bridge
= tan(16.7°) * 30 feet
Since the log is floating on the river's surface, these two height differences will be equal:
tan(14°) * L = tan(16.7°) * 30 feet
Now we can solve this equation to find the length of the log (L). Rearranging the equation, we have:
L = (tan(16.7°) * 30 feet) / tan(14°)
Using a calculator, we can find:
L ≈ (0.3039 * 30 feet) / 0.2493
L ≈ 364.1 feet
Therefore, the length of the log is approximately 364.1 feet.