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 53° and 5°m

Answer 1

To solve this problem, we can use trigonometry.

Let's start with vessel X, which is 100m away from the base of the cliff. The angle of depression from the top of the cliff is 53°.

Let the height of the cliff be h meters.

Using trigonometry, we can set up a right triangle with the height of the cliff as the opposite side, the distance from the base of the cliff to vessel X as the adjacent side, and the angle of depression (53°) as the angle.

Therefore, we can use the tangent function:
tan(53°) = h / 100

h = 100 * tan(53°)
h ≈ 114.36m

Therefore, the height of the cliff is approximately 114.36m.

Now, let's move on to vessel Y, which is 133m away from the base of the cliff. The angle of depression from the top of the cliff is 5°.

Using the same trigonometric approach:
tan(5°) = h / 133

h = 133 * tan(5°)
h ≈ 11.63m

Therefore, the height of the cliff is approximately 11.63m.

To calculate the angle of depression of vessel X and Y from the top of the cliff, we can use the inverse tangent function:
For vessel X:
θ = tan^(-1) (114.36 / 100)
θ ≈ 48.99°

For vessel Y:
θ = tan^(-1) (11.63 / 133)
θ ≈ 4.99°

Therefore, the angle of depression of vessel X from the top of the cliff is approximately 48.99° and the angle of depression of vessel Y is approximately 4.99°.