What is the value of Sin D?(24)/(7) or (7)/(24) or (24)/(25) or (7)/(25)

Question

what is the value of Sin D?
`(24)/(7) or (7)/(24) or (24)/(25) or (7)/(25)`

Answer 1

Sin D = 7 / 25

Explanation:

The value of sin D is given by

`\sin D=\frac{\text{opposite}}{\text{hypotenuse}}`
`\sin D=(EF)/(25)`

but we need to find the length EF.

Now the Pythagoras' theorem says

`EF^2+24^2=25^2`

Solving for EF gives

`EF^2=25^2-24^2`
`EF^2=49`

taking the square root of both sides gives

`EF=\sqrt[]{49}`
`EF=7`

With the value of EF in hand, we now have

`\sin D=(EF)/(25)=(7)/(25)`
`\boxed{\sin D=(7)/(25)\text{.}}`

which is our answer!