Question

please help. i have no clue how to find the measure of each unknown variable using the pythagorean theorem. any tips will be appreciated <3 :)))

Answer 1

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.

`\tan(57) = (opposite)/(adjacent) \\ = (6)/(x) \\ x \tan(57) = 6 \\ x = (6)/( \tan(57) ) \\ = 3.89645`

Since now we know x, we can then use pythogoras theorem to find y.

By pythagoras theorem,

`{y}^(2) = {x}^(2) + 6 {}^(2) \\ {y}^(2) = (3.89645) {}^(2) + 36 \\ y = \sqrt{ {3.89645}^(2) + 36 } \\ = 7.15418`

Finding Z is easy. We know that this is a triangle, which means

`z + 90 + 57 = 180 \\ z = 180 - 90 - 57 \\ = 33`