Question

the angle lf elevation between fishing vessel and the top of a 50 meter tall light house is 12 degrees. what is the approximate distance between the fishing vessel and the base of the light housee

Answer 1

235 m (3 sf)

Explanation:

See attached diagram for a visual representation of the problem, where F is the fishing vessel and b is the distance between the fishing vessel and the base of the lighthouse.

To calculate b we can use the sine rule formula:
`(a)/(sinA) =(b)/(sinB) =(c)/(sinC)`

This rule gives the ratio of the sides and angles of a triangle, where A, B, and C are the angles of the triangle and a, b, and c are the sides of the triangle that are opposite to the corresponding angles.

From the diagram and using the sine rule, we can say that:

`(50)/(sin12) =(b)/(sinB)`

However, we need with the value of angle B or the length b to proceed with solving this.

We can calculate angle B because we know the other 2 angles of the triangle and also know that the sum of the interior angles of a triangle = 180°.

Therefore, B = 180 - 90 - 12 = 78°

Substituting B = 78° into the
`(50)/(sin12) =(b)/(sinB)`:
`(50)/(sin12) =(b)/(sin78)`

multiplying both sides by sin 78:
`b=(50)/(sin12) * sin78`

Therefore, b = 235.2315055... = 235 m (to 3 significant figures)