Answer:
[tex] a = 4 [/tex]
[tex] b = 2\sqrt{3} [/tex]
Step-by-step explanation:
✔️Solving for a using trigonometric ratio:
reference angle = 60°
hypotenuse = a
adjacent = 2
Thus:
[tex] cos(60) = \frac{2}{a} [/tex]
[tex] \frac{1}{2} = \frac{2}{a} [/tex] (cos 60 = ½)
Cross multiply
[tex] 1*a = 2*2 [/tex]
[tex] a = 4 [/tex]
✔️Solving for b using trigonometric ratio:
reference angle = 60°
Opposite = b
Adjacent = 2
Thus:
[tex] tan(60) = \frac{b}{2} [/tex]
Multiply both sides by 2
[tex] tan(60)*2 = \frac{b}{2}*2 [/tex]
[tex] tan(60)*2 = b [/tex]
[tex] \sqrt{3}*2 = b [/tex] (tan 60 = √3)
[tex] 2\sqrt{3} = b [/tex]
[tex] b = 2\sqrt{3} [/tex]
