Please help! I do not know how to find the unknown variables using the Pythagorean theorem. Any help will be greatly appreciated:))

x = 13·568, y = 8·47 and z = 58

Step-by-step explanation:

I don't think the question required you to use the Pythagoras theorem but here are some pointers anyway.

The reason I said that this question might not solely require you to use the Pythagoras theorem is because you need to have two variables for the equation to work, maybe this is what got you confused.

For this question, you're required to use Tangents, Sines and Cosines, or you can combine this method and Pythagoras method.

Method one: Using Tangents, Sines and Cosines AND the Pythagoras theorem

Step 1: Looking for x(Using Sin, Cos and Tan)

To find the length of side x, we need to use the Cosine of 32°

Cos 32° = Adjacent side ÷ Hypotenuse

0·8480 = x/16

Make x the subject and multiply both sides by 16

0·8480 × 16 = x/16 × 16

13·568 = x

∴ side x is 13·568

Step 2: Looking for y( using the Pythagoras theorem)

a² + b² = c²

a = y, b = x = 13·568, c = 16

y² + 13·568² = 16²

y² + 184·0906 = 256

y² = 256 - 184·0906

y² = 71·9094

y = √71·9094

y = 8·4799

Method 2: Using Tan, Cos and Sin only

Step 1 remains the same as shown above; x = 13·568

Step 2: Looking for y

Y can be gotten by using the Sine of 32°

Sin 32° = Opposite ÷ Hypotenuse

Sin 32° = y ÷ 16

0·5299 = y/16

Make y the subject and divide both sides by 16

0·5299 × 16 = y/16 × 16

8·4784 = y

∴ y is equal to 8·4784

(I know there's a difference in points of the two values of y, but if you round them off to 2 decimal places we see it remains 8·47

   2. Looking for z:

Using addition and subtraction

The simpler method would be to just add all the internal angles.

32 + 90 + z = 180

122 + z = 180

z = 180 - 122

z = 58

∴ z is equal to 58°

Using Tan, Sin and Cos

The cosine of Z is equal to y divided by 16, where y = 8·47

Cos z = 0·5294

Make z the subject and divide both sides by Cos.

z = 0·5294/Cos

z = 58·04° (I just used the anti-cos to get this number. Press shift, and cos on your calculator then type 0.5294 in front of it)

Here there is also a slight difference in points between the two steps but if you round off step 2 to a whole number you get 58, so it's all good :)

HOPE THIS HELPS!!! :)

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option