# Thread: Trigonometry Word Problem ... Question 1

1. ## Trigonometry Word Problem ... Question 1

The following questions are for a final class project. Obviously these questions are very hard, and I am unsure how to completely answer these with the proper and complete work shown. Help on answering these questions with work/ steps would be greatly appreciated.

4. A carpenter designs a house that is 25m wide. The rafters holding the roof meet at an angle of 100°. One rafter is 23m long and its opposite angle is 60°. The carpenter wants to extend the rafters (by the same amount) past the house. How much should the rafters be extended past the house? Then find the length of the other rafter?

2. 4. A carpenter designs a house that is 25m wide. The rafters holding the roof meet at an angle of 100°. One rafter is 23m long and its opposite angle is 60°. The carpenter wants to extend the rafters (by the same amount) past the house. How much should the rafters be extended past the house? Then find the length of the other rafter?

Alright so I drew a diagram of this situation (not exactly sure how to attach it to this post), but all I managed to find was the angle 20 ° using AST.
A = 180° - 100° - 60°
A = 20° (AST)
I have absolutely no idea what to do next. Is my diagram even correct?

3. Originally Posted by shadow6
4. A carpenter designs a house that is 25m wide. The rafters holding the roof meet at an angle of 100°. One rafter is 23m long and its opposite angle is 60°. The carpenter wants to extend the rafters (by the same amount) past the house. How much should the rafters be extended past the house? Then find the length of the other rafter?

Alright so I drew a diagram of this situation (not exactly sure how to attach it to this post), but all I managed to find was the angle 20 ° using AST.
A = 180° - 100° - 60°
A = 20° (AST)
I have absolutely no idea what to do next. Is my diagram even correct?
It looks like the diagram is correct. In this case I would use the Sine Rule.

Let's call the unknown length of the rafter $y$.

This gives you the equations $\frac{\sin{60}}{23} = \frac{\sin{100}}{25+2x} = \frac{\sin{20}}{y}$

You should be able to work this out.

Remember for non-right-angled triangles you will need to use either the Sine or Cosine Rule.

4. After using the Sine law, my results were:

The rafters should extend .58m past the house and the length of the other rafter is 9.1m.

Tyvm for the help.