# Triangle Solution word problem

• May 26th 2012, 09:02 PM
GAVREED2
Triangle Solution word problem
Hi,

I'm hoping someone can help me figure out this question.

All i can basically get so far is Distance = speed * time, 16*0.25 = 4km

This gives a 4km length for the distance tarvelled but i have no idea how to find any other lengths. Especially Part B

Attachment 23965
• May 26th 2012, 09:23 PM
Prove It
Re: Triangle Solution word problem
You have the distance between the ships as 4km. It's also relatively easy to see that the angles in the triangle are \displaystyle \begin{align*} 20^{\circ}, 153^{\circ}, 7^{\circ} \end{align*}. This is enough information to use the Sine Rule to evaluate the length from where the ship started to the lighthouse.

Once you have that length, it becomes the hypotenuse of a right angle triangle with d as the vertical length and an adjacent angle of \displaystyle \begin{align*} 70^{\circ} \end{align*}. You should be able to evaluate that distance.
• May 26th 2012, 11:21 PM
GAVREED2
Re: Triangle Solution word problem
okay tha t makes sense. Just clarify how did you determine that the angles in the triangle are 153 and 7?? I get the 90-70=20 but the 7degrees i'm not so sure of
• May 27th 2012, 12:25 AM
Prove It
Re: Triangle Solution word problem
Quote:

Originally Posted by GAVREED2
okay tha t makes sense. Just clarify how did you determine that the angles in the triangle are 153 and 7?? I get the 90-70=20 but the 7degrees i'm not so sure of

The obtuse angle is 90 + 63, and the remaining angle you find from the fact that the three angles in a triangle add to 180.