# Trig triangle problem

#### helpmeddddd

A student is talented in furniture making and has decided to build a bike frame out of wood. The student likes this design they found online, but instead of curves on the frame, the student will use straight pieces of wood. As the student intends to use a wooden bike to demonstrate some woodworking skills and promote his business, they will place a triangular sign inside the frame. The sign must have an area of at least 800 cmÂ². the student has taken some measurements from the old steel road bike and will use these when they create his new wooden masterpiece.

1. Find other crucial dimensions.

My angle is 70 degrees, side length is 23.68? and the area is 800$cm^2$. How do I use this information to find the other sides etc?

#### Attachments

• 8.3 KB Views: 6
• 8 KB Views: 2
Last edited by a moderator:

#### skipjack

Forum Staff
Apply this area formula to the triangular sign to find the length of its horizontal side if the sign's area is 800 cmÂ².

#### helpmeddddd

Sorry for taking so long is this right? refer to my attachments. 2-3 are for the side lengths and the first attachment is for the angle? I tried doing it with sine but couldn't??

#### Attachments

• 17.4 KB Views: 3
• 16.2 KB Views: 4
• 6.2 KB Views: 2

#### skipjack

Forum Staff
I tried doing it with sine but couldn't??
I did 2*800/(38.68161sin(70Â°)) = 44.01793, so your value of 44.02 is correct (to 4 significant figures), as are your other values. I suggest that you label the original diagram instead of creating a new diagram without labels.

The calculated values relate to the smallest possible triangular sign.

1 person

#### helpmeddddd

Is my other side length right? and angles?

#### skipjack

Forum Staff
I've already stated that they are.

1 person