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

$\\ \sf\longmapsto tanC=\dfrac{Perpendicular}{Base}$

• <C=12°

$\\ \sf\longmapsto tan12=\dfrac{AB}{BC}$

$\\ \sf\longmapsto BC=\dfrac{AB}{tan12}$

$\\ \sf\longmapsto BC=\dfrac{50}{0.2125565616700}$

$\\ \sf\longmapsto BC\approx 235m$

Answer 2

Answer:

Distance is approximately 240 meters

Step-by-step explanation:

» From trigonometric ratios of tan:

${ \tt{ \red{ \sin( \theta) = \frac{opposite}{hypotenuse} }}}$

→ Opposite is height, 50 metres

→ Hypotenuse is d

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