Question

from a vertical cliff 80 m above sea level a fishing boat is observed at an angle of depression of 6 degrees . how far out to sea is the boat?

Answer 1

Answer:

The boat is 8.4m out of the sea

Step-by-step explanation:

Kindly find attached rough sketch of the problem.

From the sketch we can see that the observer from the cliff and the horizontal distance forms a right angle triangle

Let the horizontal distance be x

Let the angle of elevation from the boat be y

Applying sum of angles in a triangle

90+6+y= 180

96+y=180

y=180-96

y= 84°

Applying SOH CAH TOA

Using TOA

Tanθ= opposite /adjacent

Tan 84= 80/x

x= 80/tan 84

x= 80/9.51

x= 8.4m