Answer:
x = 16
y = 20
Step-by-step explanation:
the left part of the triangle can be solved first as it already has one angle and 1 side, we use trigonometry for this.
since we have 2 sides and 1 angle, to find the third side length we use the pythagoras theorem. a² + b² = c²
; 9² + 12² = c²
; 225 = c²
;√225 = c
; 15 = c
since we have all the lengths of the triangle, we can find out the angle opposite to the side length '9',
; [tex]\frac{Sin x}{9} = \frac{sin90}{15}[/tex]
; [tex]\frac{Sin 90}{15}[/tex] x 9 = Sinx
36.86 = x
now, we look at the triangle as a whole, the top angle being 90 degrees, we know that we have 36.86.
; 90 - 36.86 = 53.13
[tex]\frac{y}{Sin 90} = \frac{12}{Sin 36.86}[/tex]
; [tex]\frac{12}{sin 36.86}[/tex] x Sin 90 = 20
y = 20
again, since we have 2 sides of a right angled triangle we use a² + b² = c²
we arrange this formula since we have the hypotenuse
; 20² - 12² = 256
; √256 = x
; 16 = x
