Question

What is the value of side c?

Please help Im clueless and have been consulting the book for almost an hour now.

Answer 1

`c = 20`

Explanation:

`c` is `20` because

`sin(C)` is `5/6`

Sine is also known as

`"opposite"/"hypotenuse"`

`5` would be the opposite side from `"point C"`, and `6` would be the `"hypotenuse"`. It also tells us `b` is `24`.

In our ratio of `"side c"` to `"side b"`, we know it is `5/6`, so we can rewrite it as

`5/6 = x/24`

Multiplying `5/6` by `24` to isolate `x`, we get `(5*24)/6 = x`

`120/6` equals `x`, and finally we get `20 = x`, giving us `"side c"`, or the longer leg, as `20`.

Answer 2

`20` units

Explanation:

Let's start with the equation we have:

`sin(C)=5/6`

We can take the inverse `sin` (`arcsin`) to solve for angle C, which will help us solve for side c.

`arcsin(sin(C))= arcsin(5/6)` (`arcsin` cancels with `sin`)

`C~~0.985` radians (`56.44269024` degrees)

`C=56.44269024` degrees. Relative to angle C, side c is the opposite side, and side b is obviously the hypotenuse. We can use the mnemonic SOH-CAH-TOA:

SOH- Sine=opp/hyp
CAH- Cosine=adj/hyp
TOA- Tangent= opp/adj

Sine is the trig ratio that uses opposite and adjacent. Now, we can set up our equation:

`sin(56.44269024)=c/24`

We can multiply both sides by `24` to isolate c, and we get:

`c=24sin(56.44269024)`

`c=20` units