Step-by-step explanation:
To be honest for this question you DO NOT have to use pythagoras theorem , and you can't either as you won't be able to start.
I have a method called the TOA CAH SOH method, which comprises 3 formulas,
TOA (tangent = opposite/adjacent)
CAH (cosine = adjacent/hypotenuse)
SOH (sine = opposite/hypotenuse)
In this case we will solve the question in alphabetical order starting with x.
for x, we can use TOA.
[tex] \tan(57) = \frac{opposite}{adjacent} \\ = \frac{6}{x} \\ x \tan(57) = 6 \\ x = \frac{6}{ \tan(57) } \\ = 3.89645[/tex]
Since now we know x, we can then use pythogoras theorem to find y.
By pythagoras theorem,
[tex] {y}^{2} = {x}^{2} + 6 {}^{2} \\ {y}^{2} = (3.89645) {}^{2} + 36 \\ y = \sqrt{ {3.89645}^{2} + 36 } \\ = 7.15418[/tex]
Finding Z is easy. We know that this is a triangle, which means
[tex]z + 90 + 57 = 180 \\ z = 180 - 90 - 57 \\ = 33[/tex]
