Question

What is the value of x?

enter your answer in the box


x = [ ]

Answer 1

Attached the solution. It is important to know the 30-60-90 and 45-45-90 special right triangles.

Answer 2

`x=4`

Explanation:

We have been given an image of two right triangles and we asked to find the value of x.

First of all , we will find the length of segment RT using sine.

`\text{Sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

Upon substituting our given values in above formula we will get,

`\text{Sin}(60^(\circ))=(2√(3))/(RT)`

`RT=\frac{2√(3)}{\text{Sin}(60^(\circ))}`

`RT=(2√(3))/((√(3))/(2))`

`RT=(2√(3))/(√(3))* 2`

`RT=2* 2`

`RT=4`

Now we know that length of segment RT and angle QRT of triangle QRT, so we will use tangent to find the length of segment QR (x) as:

`\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

`\text{tan}(45^(\circ))=(x)/(4)`

Multiplying both sides of our equation by 4 we will get,

`\text{tan}(45^(\circ))*4=(x)/(4)*4`

`\text{tan}(45^(\circ))*4=x`

Substituting
`\text{tan}(45^(\circ))=1` we will get,

`1*4=x`

`4=x`

Therefore, the value of x is 4 units.