Question

Find the values of x and y in the diagram.

Answer 1

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) = (x - 7)/(11 + x - 7 ) \\ \sin(30) = (x - 7)/(x + 4) \\ 0.5 = (x - 7)/(x + 4) \\ 0.5(x + 4) = (x - 7) \\ 0.5x + 2 = x - 7 \\ 0.5x = 9 \\ x = 18`