Question

Write a equation that will help you solve for d using the ratio sin40

Answer 1

do you know soh cah toa ?

Answer 2

yeah i am supposed to use soh to figure this out so it would be opposite/hypotenuse

Answer 3

unless my last question was wrong and the right answer is cah

Answer 4

you are given the hypotenuse of "40", and also it's opposite, so

Answer 5

so it is soh?

Answer 6

yes

Answer 7

opposite means you can draw an arrow from the angle to the other side:

Answer 8

notice the hypotenuse is opposite the right angle (the 90º angle)

Answer 9

now you know to use soh sin(angle) = opposite/hypotenuse
replace angle with 40, replace opposite with 200, replace hypotenuse with d

Answer 10

how would i then solve that?

Answer 11

first, what do you have ?

Answer 12

sin (40) = 200/ d

Answer 13

@phi

Answer 14

yes. to solve, I like the "d" up top. one way to get the d up top is multiply both sides by d
\[ d \cdot sin(40) = \frac{200}{d} \cdot d \]
can you simplify the right hand side ?

Answer 15

remember you can swap the order of the multiplies . keep the top 200 * d
but sway d*1 to 1*d
\[ \frac{200}{d} \cdot \frac{d}{1} =\frac{200}{1} \cdot \frac{d}{d} \]
d/d is 1 , right ?

Answer 16

and 200/1 * 1 is just 200

Answer 17

you get
\[ d \sin(40) = 200\]
now divide both sides by sin(40) to get d by itself.
to get a number, you will need to use a calculator.

Answer 18

200 divided by 40 is =5

Answer 19

and on the other side 40 will just cancel out right so what we will have is d=5? @phi

Answer 20

right idea, but sin(40) is not 40. get a calculator or use google: type this into the search window
sin(40 degrees)=

Answer 21

how would i type this into my calculator

Answer 22

try sin 40 enter

Answer 23

or sin 40 =

Answer 24

ok i did

Answer 25

what did you get ?

Answer 26

d= 200/sin(40)

Answer 27

i got .64278

Answer 28

yes, and d= 200/ugly number

Answer 29

312.5

Answer 30

I am getting something slightly smaller.
don't round
type in
200
/
sin
40
=

Answer 31

oh ok i got 311.144

Answer 32

yes.

as a check, if we do
inverse sin( 200/311.144) we should get back 40 degrees (or close to it)