Question

Find the value(s) of the variable(s). Write your answer(s) in simplest radical form.

Answer 1

Explanation:

12). By applying Pythagoras theorem in the given right triangle,

Hypotenuse² = (Leg 1)² + (Leg 2)²

x² = 7² + 7²

x² = 2(7)²

x =
`\sqrt{2(7)^(2) }`

x =
`7√(2)`

13). By sine rule,

sin(60)° =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

`(√(3))/(2)=(9√(3) )/(y)`

y =
`(18√(3) )/(√(3) )`

y = 18

By cosine rule,

cos(60)° =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

`(1)/(2)=(x)/(y)`

x =
`(y)/(2)`

x =
`(18)/(2)=9`

14). By applying Pythagoras theorem in the given right triangle,

12² = x² + x²

144 = 2x²

72 = x²

x = √72

x = 6√2