Question

Helppp mee please ive been trying to get this for a while now

Answer 1

`sin(P)=(√(55))/(10)`

Explanation:

Sine Function:

The sine function is defined as a ratio of sides:
`sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}`

where the "opposite" side is quite literally the opposite side, if you went straight from the angle, whatever side it's pointing towards is the opposite angle. The hypotenuse... is as the name implies, the hypotenuse. The symbol inside the parenthesis next to the sine is called theta and is just used to represent some angle.

We of course don't know the hypotenuse as it's not given, but we can use the Pythagorean Theorem to solve for the hypotenuse:

`c^2=√(45)^2+√(55)^2\\c^2=45+55\\c^2=100\\c=10`

We do know the opposite side though, it's just the square root of 55, it's directly opposite of the angle P. Plugging in known values we get the following:
`sin(P)=(√(55))/(10)` and we can't simplify this any further as 45 has no factors which are perfect squares.