Question

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

Answer 1

Answer:
`\bold{(A): g=(√(15))/(2),\quad h=(√(5))/(2)}`

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=√(5)`

`a=(√(5))/(2)`

According to your picture, a = h, so
`h=(√(5))/(2)`

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

`g=a√(3)`

`=\bigg( (√(5))/(2)\bigg)√(3)`

`=(√(15))/(2)`