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?

4.2 inches

5.7 inches

2.5 inches

1.3 inches

Answer 1

@hartnn

Answer 2

hint : in a 45-45 Right triangle,
both legs are equal!

Answer 3

that will give you AB

Answer 4

what do u mean by "both legs"

Answer 5

2 sides of right triangle ABC

Answer 6

so then AB is 10 ?

Answer 7

yes

Answer 8

side opposite to 60 degree angle is sqrt 3/2 times the hypotenuse

thats gives you CD in triangle BCD

Answer 9

60 degree angle ?

Answer 10

angle D in triangle BCD = 60

Answer 11

why is it sqrt 3/2 ? (sorry for many questions)

Answer 12

property of a 30-60-90 triangle

you can prove that using trigonometry

Answer 13

do u have to use trigonometry ?

Answer 14

yes

Answer 15

ok,
then tan 30 =... ?
in triangle BCD

Answer 16

opp over adj... idk opp.... adjacent is 10

Answer 17

right
you need to find BD , which is opposite side
and tan 30 = sqrt 3

Answer 18

sqrt 3 = BD/10

Answer 19

how do i find bd ?

Answer 20

multiply 10 on both sides

Answer 21

17.32 ?

Answer 22

keep it as 10 sqrt 3
or
17.32 is also correct

Answer 23

AD = AB-BD

Answer 24

sorry, tan 30 = 1/sqrt 3 = 0.557

Answer 25

BD = 5.57

Answer 26

AD = 10 -5.57

Answer 27

4.43 ..

Answer 28

its not in my answers

Answer 29

4.23

Answer 30

is the nearest option

Answer 31

take tan 30 approximately as 5.8

Answer 32

how come i didnt get 4.23 ?

Answer 33

take the approximate value

Answer 34

ohhh ok 4.23 it is.. thank you! btw i was telling someone in chat to not post questions there and some person kept calling me a snitch and stuff.... her account is shadowgirl15

Answer 35

welcome ^_^
thanks for informing :)

Answer 36

:D np