Question

Part 1: Make up an angle measure for angle C and a length for one of the sides (AB, BC, or CA).

Part 2: Use a trigonometric ratio (sine, cosine, or tangent) to solve for one of the other side lengths.

For full credit, please provide both the ratio and work used to solve for the missing side length. Round your solution to the nearest hundredth.

Answer 1

ok pick a number. make it easy say between 40 and 70

Answer 2

45

Answer 3

too easy but that is ok we can use that one

Answer 4

what must the other angle be?

Answer 5

i believe the same as the first angle

Answer 6

yes, they are both 45 because the total must be 90

now you have to pick a length of one side or of the hypotenuse
what do you pick?

Answer 7

27 or is that to easy?

Answer 8

any number you like, 27 is fine
what side do you want it to be?

Answer 9

the side of BC

Answer 10

not sure what side that is. is it the hypotenuse or one of the two legs of the triangle?

Answer 11

sorry i forgot to attach the picture but its one of the legs

Answer 12

ok now the reason i said this was too easy when you picked 45 is that there is really not much trig you need here
since both angles are equal, this is an isosceles triangle, therefore of one let is 27 what must the other leg be?

Answer 13

would the be the same as the first leg? I mean they look like they would be the same. cause thats the part i got stuck on.

Answer 14

yes they would be the same because of the two angles are equal, the two sides must be equal as well

Answer 15

and the hypotenuse you can find by by pythagoras
\[h^2=27^2+27^2\]
\[h=\sqrt{2\times 27^2}=27\sqrt{2}\]

Answer 16

that is why i said this was too easy, we didn't use sines or cosines
do you have to hand this in? in which case we should pick another angle, something other than 45 degrees
say 40 degrees

Answer 17

okay and yeah its a question in my test on flvs

Answer 18

ok so lets start again this time with 40 degrees and you will get an A
i will make the picture look like yours

Answer 19

now this time what is the other angle?

Answer 20

50?

Answer 21

yes! they have to add up to 180 and you already have 90 + 40 that leaves 50

Answer 22

now pick the length of a side
pick a nice round number

Answer 23

30=bc?

Answer 24

ok fine 30 will do nicely

Answer 25

you understand of course that 30 means say 30 inches, it is not the measure of an angle but rather a length
now you can use any trig ratio you like to find the other sides

Answer 26

lets call the hypotenuse \(h\) and the adjacent side \(a\) and label so we can solve for \(a\) and also \(h\)