SET of 3! Please help

1. 24/40, 32/40, 24/32 (This is in order from top to bottom)

2. 21.1

3. 4.1

Step-by-step explanation:

1. Here, we only have to focus on Angle X.

Let's label in the sides:

Opposite = YZ = 24

Adjacent = XY = 32

Hypotenuse = XZ = 40

SOHCAHTOA simply means:  You can memorise this through the acrostic poem of - Slap On Head Causes A Headache Take One Aspirin, but I remember it by Suck A Toe because that's what it sounds like.

Sin(x) = Opposite/Hypotenuse

Cos(x) = Adjacent/Hypotenuse

Tan(x) = Opposite/Adjacent

Sin(X) = 24/40

Cos(X) = 32/40

Tan(X) = 24/32

The question only asks to give the ratios by using / for a fraction, so we don't simplify it.

2. We are given the angle of 64°, the opposite length 19 and we have to work out x, which is the hypotenuse. We can use the sin function as we have our opposite length and we have to work out the hypotenuse.

Sin(64) = 19/x

xSin(64) = 19

x = 19/Sin(64)

x = 21.13943687

x = 21.1

3. We are given the angle of 70°, the hypotenuse 12 and we have to work out x, which is the adjacent side. We can use the cos function as we have to work out the adjacent side and we have our hypotenuse given to us.

Cos(70) = x/12

12Cos(70) = x  All we have to do here is multiply by 12!

x = 4.10424172

x = 4.1

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