Question

Fill in the blank. In the triangle below, y=__. Round your answer to two decimal places.

Please explain, thank you.

Answer 1

What side of the triangle is Y ?

Answer 2

did you see the attachment

Answer 3

Yes i m asking you like the name of the side

Answer 4

oh ok so hypotenuse then

Answer 5

Yup! Okay now we use the Pythagorean theorem

Answer 6

a^2+b^2=c^2

Answer 7

so do we fill in the information we already have into this formula

Answer 8

i think i made a mistake . We dont use the theorem we use Sine

Answer 9

Do you have a calculator ?

Answer 10

yes

Answer 11

We know one angle measure beside 90 . That angle is 52

Answer 12

So type 52 then hit sine

Answer 13

sin(52) = 0.788010754

Answer 14

I got 0.98662759204

Answer 15

oh ok im not sure why i got that i pressed sin(52) and got 0.788

Answer 16

I think your right though

Answer 17

yeah i checked online it is

Answer 18

Yup i tried it on another calculator your right :)

Answer 19

Sine = opposite / hypotenuse

Answer 20

Plug our values into that

Answer 21

the opposite is 35 but the hypotenuse is y on the picture

Answer 22

0.788010754 = 35/y

Answer 23

im still confused about the y part what is y?

Answer 24

In your picture the hyotenuse was labeled Y

Answer 25

yeah but on the formula Sine = opposite / hypotenuse or 0.788010754 = 35/y don't you need to plug in something for y to solve

Answer 26

We dont have the value of y . Were using that equation to find the value of y

Answer 27

oh ok

Answer 28

So now what do you get ?

Answer 29

y=35/sin(38°)=56.85

Answer 30

Where did sin 38 come from

Answer 31

the 38 degrees is a result of 180°-52-90=38 being that a triangle is 180 degrees I subtracted 52 and 90

Answer 32

You dont do sine again . Just do regular algebra to find y in the equation 0.788010754 = 35/y

Answer 33

I got 44.42

Answer 34

@dumbcow @jim_thompson5910 Could you check this please ?

Answer 35

http://cossincalc.com/#angle_a=&side_a=35&angle_b=90&side_b=&angle_c=52&side_c=&angle_unit=degree

Answer 36

hmm i think you should have used cos instead of sin
the 35 is adjacent to angle 52

Answer 37

I just right now found that website above

Answer 38

or do what @KJ4UTS did and use angle 38 :)

Answer 39

\[\sin 38 = \cos 52 = \frac{35}{y}\]
\[y = \frac{35}{\sin 38} = \frac{35}{\cos 52}\]

Answer 40

i got 56.84942359 for both and if it says round two decimal places I guess that makes the answer 56.85 i think?

Answer 41

Yes rounded its 56.85