### 3 Answers

- ?Lv 71 month agoFavourite answer
Right Scalene Triangle

Side x = 18

Side z = 15.09607

Side w = 9.8035

Angle ∠X = 90°

Angle ∠Z = 57°

Angle ∠W = 33°

- 1 month ago
I'm assuming your goal is to complete the triangle by filling in the missing angle and the side lengths....

Facts to know: the interior angles of any triangle add to 180 degrees.

soh cah toa

sin theta = opp/hypotenuse etc.

angle w is going to be 180-90 -57= 33 degrees

once you have all three angles and at least one side the remaining sides can be figured out using trigonometry soh cah toa

using these identities choose one that contains 2 of the three variables angle and two sides.

note* calculators with trig functions can be set in two modes, degrees and radians this problem calls for degrees and check to see its in the right mode. if a problem is in radians the rotational measure will use pi and be called rad or radians..

we already know each angle and the hypotenuse.

if we take sin 57 (angle z chosen as the reference angle) we get the proportion of the opposite side over the hypotenuse. meaning sin 57 = opp/18

with a little bit of algebra we can multiply both sides by 18 making the opposite side of angle z side equal to 18*sin57.

you can use the exact same method using the sine function but instead using angle W as the reference angle..

Hope this helps.

Source(s): Math major