Question

4) A man standing on a cliff looks down with an angle of depression of 40 degrees to a boat in

the water below the cliff. The cliff is 80m high and the man's eye's are 1.5m above the cliff. How
far from the cliff wall is the boat?

Answer 1

To calculate the distance from the cliff wall to the boat, we can use trigonometry and the angle of depression.

Step-by-step explanation:

To solve this problem, we can use trigonometry. Let's define some variables:

H = height of the cliff

d = distance from the cliff to the boat

x = horizontal distance from the man to the boat

Using the angle of depression, we have:

tan(40 degrees) = H / x

From the given information, we can calculate H:

H = 80m + 1.5m = 81.5m

Substituting this into the equation for tangent:

tan(40 degrees) = 81.5 / x

Solving for x:

x = 81.5 / tan(40 degrees)

Using a calculator, we find that x is approximately 93.21m.

Answer 2

Distance between boat and cliff (Base) = 97 m (Approx)

Step-by-step explanation:

Given:

Angle of depression = 40°

Height of cliff = 80 m

Height of man's eye's from cliff = 1.5 m

Find:

Distance between boat and cliff (Base) :

Computation:

Total height (Height) = 80 m + 1.5 m = 81.5 m

Using trigonometry application:

`Tan\theta = (Height)/(Base) \\\\Tan \ 40 = (81.5)/(Base) \\\\Using\ calculator\ to\ find\ the\ value\ of\ Tan 40\\\\Tan 40 = 0.839\\\\0.839=(81.5)/(Base)\\\\Base = 97.139`

Distance between boat and cliff (Base) = 97 m (Approx)