Question

I keep getting .13 but it's wrong. The figure shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced. What is the length of the wood that is needed to replace AD?
1.3
2.5
4.2
5.7

Answer 1

@gymnastkitkat Can you find AB?

Answer 2

You know what AB is, since ABC is an isosceles triangle.
Side DB = half of the hypotenuse DC, since DBC is a 30-60-90 triangle.
Simply subtract DB from AB to find AD.

Answer 3

I'm still confused :/

Answer 4

Well, since ABC is a 45-45-90 triangle, or an isosceles triangle, it's two legs (AB & BC) must have the same length. Therefore, AB = BC = 10 inches. Make sense so far?

Answer 5

yeah

Answer 6

So, assuming you understand that 30-60-90 triangles have sides with the ratios x, x sqrt(3), and 2x, like this:Then we know that \[10 = x \sqrt{3}\]or basically, since DB = x, \[DB = x = {10 \over \sqrt3}\]So your final answer is\[AD = AB-DB = 10 - {10 \over \sqrt3}\]

Answer 7

Oh ok I get it now thank you!