First, we need to calculate the height of the cliff.
Let h be the height of the cliff.
For vessel X, the angle of depression will be the angle formed by the line from the top of the cliff to vessel X, and the horizontal line parallel to the ground.
Therefore, tan(angle_X) = h/100
For vessel Y, the angle of depression will be the angle formed by the line from the top of the cliff to vessel Y, and the horizontal line parallel to the ground.
Therefore, tan(angle_Y) = h/133
From the question, the height of the cliff h is given as 53m. So for vessel X:
tan(angle_X) = 53/100
angle_X = tan^(-1)(53/100)
For vessel Y:
tan(angle_Y) = 53/133
angle_Y = tan^(-1)(53/133)
Calculating angle_X and angle_Y gives:
angle_X ≈ 26.6 degrees
angle_Y ≈ 21.7 degrees
Therefore, the angle of depression of vessel X from the top of the cliff is approximately 26.6 degrees and the angle of depression of vessel Y from the top of the cliff is approximately 21.7 degrees.
two vessels x and y are 100m and 133m away from the base of a cliff respectively. calculate the angle of depression of the vessel's from the top of the 53m and 5m
1 answer
1 answer