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 house

Answer 1

For diagram and better understanding refer to the attachment.

Here

• AB is the height of lighthouse=50m
• Distance from base of lighthouse and fishing vessel is BC

Now

As per we know

`\\ \sf\longmapsto tanC=(Perpendicular)/(Base)`

• <C=12°

`\\ \sf\longmapsto tan12=(AB)/(BC)`

`\\ \sf\longmapsto BC=(AB)/(tan12)`

`\\ \sf\longmapsto BC=(50)/(0.2125565616700)`

`\\ \sf\longmapsto BC\approx 235m`

Answer 2

Distance is approximately 240 meters

Explanation:

» From trigonometric ratios of tan:

`{ \tt{ \red{ \sin( \theta) = (opposite)/(hypotenuse) }}} \\`

→ Opposite is height, 50 metres

→ Hypotenuse is d

`{ \tt{ \sin(12 \degree) = (50)/(d) }} \\ \\ { \tt{d = (50)/( \sin(12 \degree) ) }} \\ \\ { \boxed{ \tt{ \: d = 240.458 \approx240 \: m}}}`