Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A boat going parallel to shore spots a lighthouse ahead on shore. The angle of the line from lighthouse to boat is 30 degrees. The boat sails 3mi, and now angle is 90. How far offshore is boat?

share|improve this question
2  
Draw it out first. Can you see how the boat's path in the problem forms a triangle? –  Drew Christianson Sep 21 '12 at 20:38
    
30 degrees between the line and the shore, presumably? –  rschwieb Sep 21 '12 at 20:38

3 Answers 3

Consider the right angle triangle seen here: http://en.wikipedia.org/wiki/Right_triangle

Let, B: the location of the lighthouse, A: your past location (when the line formed an angle of 30 deg), C: your current location at 90 deg.

You know the angle at vertex A, ang(A) = 30 deg, and, b = 3mi, you are asked to determine small a. What is the relationship between ang(A), a, and b?

share|improve this answer

$\sqrt{3}$ miles. A picture helps.

share|improve this answer

Here’s a diagram of the setting:

enter image description here

You want the distance $x$. It’s the length of one of the legs of a nice right triangle, and you know the length of the other leg. If you recognize this as a $30$-$60$-$90$ triangle and know the proportions of the sides in such a triangle $-$ and this is useful information that you probably should learn $-$ then you can get $x$ immediately. If not, you’ll need to use one of the trig functions of $30$°; do you know which one is useful here?

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.