Question

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

Answer 1

Answer:

Step-by-step 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 = $7\sqrt{2}$

13). By sine rule,

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

      $\frac{\sqrt{3}}{2}=\frac{9\sqrt{3} }{y}$

      y = $\frac{18\sqrt{3} }{\sqrt{3} }$

      y = 18

      By cosine rule,

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

      $\frac{1}{2}=\frac{x}{y}$

      x = $\frac{y}{2}$

      x = $\frac{18}{2}=9$

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

      12² = x² + x²

      144 = 2x²

      72 = x²

      x = √72

      x = 6√2