Geometry/Calculus math problem ??

Question

I need to solve this problem without using a calculator:

From a small boat the angle of elevation to the top of a lighthouse is 30 degrees. How far from the foot of the lighthouse is the boat if the top of the lighthouse is 50ft above sea level?

Answer 1

this is best done if you draw a diagram. if you do, you should see that there is a right triangle formed. one leg is 50, the angle across from it is 30, and you need to find the other leg.

set up this equation:

tan30 = 50/x

then x= 50* tan30

Answer 2

Let x be the distance sought. Then 50/x = tan(30) = 1/\sqrt{3}

Hence x = \sqrt{3}50

Answer 3

sin30/50=sin60/x

50sin60=xsin30

50(sqrt3/2)=1/2x

50sqrt3=x

dunno sqrt3 off the top of my head, sorry.

make it a good day

Answer 4

dude this is trigonometry the answer is 86.65 ft

Answer 5

I hate both subjects

Answer 6

It's actually a trigonometry problem.

Set it up as a triangle, angle-side-side.  The angle is 30 degrees, the vertical (y) is 50ft, and the horizontal (x) is the unknown.

Tan(30deg) = y/x

x = y / tan(30deg) = 50ft / (0.577)

x = 86.6ft

Answer 7

tan theta = opposite/adjacent

tan 30 = 50/x

(tan 30)*x = 50

x = 50 / (tan 30)