Answer:
Step-by-step explanation:
Given triangle ABC is a right triangle.
m∠ACB = 60°
m∠CAB = 30°
m(AC) = 1 unit
A). Shorter side of the given triangle = Side BC
By applying cosine rule,
cos(∠C) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(60°) = [tex]\frac{BC}{AC}[/tex]
BC = [tex]\frac{1}{2}(AC)[/tex]
BC = [tex]\frac{1}{2}[/tex]
Length of the shorter side = 0.5 units
B). Longer side of the given triangle = side AB
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
1² = AB² + [tex](\frac{1}{2})^2[/tex]
1 = AB² + [tex]\frac{1}{4}[/tex]
AB = [tex]\sqrt{1-\frac{1}{4}}[/tex]
AB = [tex]\sqrt{\frac{3}{4}}[/tex]
AB = [tex]\frac{\sqrt{3} }{2}[/tex]
Length of the longer side = [tex]\frac{\sqrt{3}}{2}[/tex]
