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?
A.) 4.2 inches
B.) 5.1 inches
C.) 6.2 inches
D.) 6.9 inches

Answer 1

@amistre64 can you help me out im not sure wich formula to use

Answer 2

ad is the top part right?

Answer 3

yes the top left

Answer 4

whenever we have information that refers us to the sides of a rt triangle, we use the tangent function to our advantage

Answer 5

M = tan(30+15) = ab/bc

N = tan(30) = db/bc

M - N = ad

Answer 6

or simply solve for ab and db; then subtract; ab - db = ad

Answer 7

can you show me how you would do that?

Answer 8

yes let me try

Answer 9

how would i plug in the numbers?

Answer 10

you have 3 numbers to play with; 2 angles and a side

tan(30) = db/bc ; we know bc = 12

tan(30) = db/12 solve for db

12 tan(30) = db
-----------------------

tan(30+15) = ab/bc

tan(45) = ab/12

12 tan(45) = ab
-----------------------

ab - db = ad

12 tan(45) - 12tan(30) = ad

Answer 11

i got 12-4sqrrt3=ad

Answer 12

lets see what i get :)

ad = 12 - 12(1/sqrt(3))

ad = 12 - 12/sqrt(3)

ad = 12 - 4sqrt(3)

i agree

Answer 13

so the answer is B?

Answer 14

5.07 is about 5.1 , so yes

Answer 15

might have to shave it to fit perfectly :)

Answer 16

Thank you for your help :)

Answer 17

youre welcome