Question

Find the length of the side opposite the 30-degree angle in a 30-60-90triangle in which the side opposite the 60-degree angle is 12. *13 root 44 root 3(12 root 3)/root 64

Answer 1

Option B is correct

x = 4√3

Step-by-step explanation

The right angle triangle is sketched above and we will use trignometric relations to solve this.

We need the value of x,

In a right angle triangle, the side opposite the right angle is called the Hypotenuse, the side opposite the given angle (let us use 60° as the given angle) is called the Opposite and the remaining side is called the Adjacent.

For this question,

Hypotenuse = ?

Opposite = 12

Adjacent = x

Using TOA, we can say that

Tan 60° = (Opp/Adj)

tan 60° = (12/x)

Note that Tan 60° = √3

tan 60° = (12/x)

√3 = (12/x)

Cross multiply and we have

x = (12/√3)

We can then rationalize this

`\begin{gathered} x=(12)/(√(3))*(√(3))/(√(3)) \\ =(12√(3))/(3) \\ =4√(3) \end{gathered}`

x = 4√3

Hope this Helps!!!