WILL MEDAL!

Question

WILL MEDAL!

anonymous · Answer

The angle of depression from a lighthouse 250 ft high to a boat in the water is 15 degrees 20'. how far is the boat from the base of the lighthouse. Draw a picture.

valpey · Answer

|dw:1415237160826:dw|
Well, the Tangent of an angle is equal to the length of the Opposite side divided by the length of the Adjacent side.

valpey · Answer

And I'm drawing the angle of inclination from the boat's perspective which is the same as the angle of depression from the lighthouse's perspective.

anonymous · Answer

$$\tan 15 degrees 20' = 250 x$$

anonymous · Answer

= 250/x

anonymous · Answer

x = tan^-1 (15 degrees 20')250

valpey · Answer

Yes, $\tan {15^{\circ}20'} = \frac{250}{x}$
|dw:1415237443508:dw|Also the angle at B is equal to $90-15^{\circ} 20'$. The Tangent of B is equal to x/250.

anonymous · Answer

thank you so much!

valpey · Answer

Also, be careful with your "tan^-1" that usually means inverse tangent

anonymous · Answer

than how do you solve for tan15degrees20′=250/x