Question

Find x and y. give answer in insimplified radical form, not decimal.

Answer 1

Finding x,

We will use Pythagoras theorem to determine the value of x:

$9^{2} = {8}^{2} + {x}^{2} \\ 81 = 64 + {x}^{2} \\ 81 - 64 = {x}^{2} \\ {x}^{2} = 17 \\ x = \sqrt{17}$

Finding y,

We have to determine the angle, at the bottom left of the bigger triangle.

Using sine rule,

$\frac{9}{sin(90)} = \frac{8}{sin(z)} \\ sin(z) = 0.8889 \\ z = {sin}^{ - 1} (0.8889) \\ z = 62.73$

To find the angle on the smaller triangle,

$a = 90 - 62.73 \\ a = 27.27$

Finding the missing length of y,

$\frac{ \sqrt{17} }{sin(62.73)} = \frac{m}{sin(27.27)} \\ m = 2$

So y = 2 + 8, y = 10