What is the value of side c?

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

2 Answers
Feb 22, 2018

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.

Feb 22, 2018

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