Question

Identify the values of the variables. Give your answers in simplest radical form. HELP PLEASE!!!

Answer 1

Answer: $\bold{(A): g=\dfrac{\sqrt{15}}{2},\quad h=\dfrac{\sqrt{5}}{2}}$

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

$2a=\sqrt{5}$

 $a=\dfrac{\sqrt{5}}{2}$

According to your picture, a = h, so $h=\dfrac{\sqrt{5}}{2}$

Step 2: use the a-value from Step 1 to solve for the remaining side

$g=a\sqrt{3}$

   $=\bigg( \dfrac{\sqrt{5}}{2}\bigg)\sqrt{3}$

   $=\dfrac{\sqrt{15}}{2}$