Question

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?

Answer 1

@ganeshie8 ?

Answer 2

find tan 30= db /14
get value of db

then find tan (45)= ab /14

Answer 3

after finding ab, see that ab=ad+db, subtract value of db to find ad

Answer 4

does that help

Answer 5

@dorothynichole
Look at the outer triangle. It is a 45-45-90 triangle and the 45-45-90 theorem applies. Segment AB = 14.

Now look at Triangle DBC. It is a 30-60-90 triangle and that theorem applies. The 60 degree leg BC is 14. Therefore, DB has length 14/(square root of 3).

The rotten section AD is equal to AB - DB = 14 - 14/(square root of 3) =
5.917 units (approx)