Answer: [tex]\bold{(A): g=\dfrac{\sqrt{15}}{2},\quad h=\dfrac{\sqrt{5}}{2}}[/tex]
Step-by-step explanation:
This is a special triangle because the side lengths have the following relationship:
30° ⇄ side length "a" represented as "h" in your picture
60° ⇄ side length "a√3" represented as "g" in your picture
90° ⇄ side length "2a" represented as "√5" in your picture
Step 1: solve for "a" hypotenuse (2a) is given as √5
[tex]2a=\sqrt{5}[/tex]
[tex]a=\dfrac{\sqrt{5}}{2}[/tex]
According to your picture, a = h, so [tex]h=\dfrac{\sqrt{5}}{2}[/tex]
Step 2: use the a-value from Step 1 to solve for the remaining side
[tex]g=a\sqrt{3}[/tex]
[tex]=\bigg( \dfrac{\sqrt{5}}{2}\bigg)\sqrt{3}[/tex]
[tex]=\dfrac{\sqrt{15}}{2}[/tex]
