Answer:
The distance between the lighthouse and the boat is: 164.91 meters
Step-by-step explanation:
Please look at the attached image to follow the triangular diagram generated with the info provided.
Notice that we can create a right angle triangle with the information presented in the problem. The height of the lighthouse (70 m) is the side opposite to a 23 degree angle. And what we need to find is the other side "D" perpendicular to the lighthouse, which stands for the horizontal distance between the lighthouse and the boat.
Since the sides involved are the opposite and the adjacent sides to the 23 degree angle, we use the tangent function to solve it:
[tex]tan(23^o)=\frac{opp}{adj} \\tan(23^o)=\frac{70}{D}\\D=\frac{70}{tan(23^o)} \\D= 164.91\,\,m[/tex]
