Question

Please help I need to find the measure of the three unknown variables. Any help will be greatly appreciated:))

Answer 1

`x = 8 √(3)`

`y = 60`

`z = 30`

Explanation:

To find x, use pythagorean theorem,

`{x}^(2) + {8}^(2) = {16}^(2)`

`{x}^(2) + 64 = 256`

`{x}^(2) = 192`

x=13.9 or 8 times sqr root 3( see later)

To find y, use cosine ratio.

`\cos(y) = (8)/(16)`

`\cos(y) = (1)/(2)`

`y = 60`

To find z, use triangle interior theorem

`90 + 60 + z= 180`

`150 + z = 180`

`z = 30`

Since this a 30-60-90 triangle, side x could be also written as

`8 √(3)`