Answer:x = 18.5
y = 14.2
Step-by-step explanation:
The given triangle is labelled in the attached photo to make the explanations clearer.
The sum of the angles in a triangle is 180 degrees. Let the unknown angle be # degrees.
This means that
90 + 50 + 21 + # = 180
161 + # = 180
# = 180 - 161 = 19 degrees.
To determine y, we will apply trigonometric ratio
Cos # = adjacent/hypotenuse
Cos 19 = y/15
y = 15cos19 = 15 × 0.9445 = 14.2
To determine x, we will apply trigonometric ratio
Sin 50 = opposite/hypotenuse
Sin 50 = y/x = 14.2/x
xsin50 = 14.2
x = 14.2/sin50 = 14.2/0.7660 = 18.5
