Question

Find the values of x and y in the diagram.

Answer 1

Step-by-step explanation:

the triangle URT is an Equilateral triangle so all angles are equal to 60°

and the full triangle UTS is a right angle .

5y= 90-60= 30°

y= 6

and since the triangle RST is an Isosceles triangle

so the angle RST and RTS are equal .

in this case =30° .

$\sin(30) = \frac{x - 7}{11 + x - 7 } \\ \sin(30) = \frac{x - 7}{x + 4} \\ 0.5 = \frac{x - 7}{x + 4} \\ 0.5(x + 4) = (x - 7) \\ 0.5x + 2 = x - 7 \\ 0.5x = 9 \\ x = 18$