Question

Find w.

3-√2 mm
45°
W
45°
Write your answer in simplest radical form.
millimeters

Answer 1

The value of w shown in the right angle triangle is calculated to be 3 millimeters

How to calculate the value of w?

From the diagram shown above, the following parameters were obtained:

• Angle θ = 45 degree
• Hypotenuse =
  `3√(2)` mm
• Value of w = Opposite = ?

We can calculate the value of w by using the the trigonometry ratio of Sine θ. This is sillustrated below:

`Sine\ \theta\ = (Opposite)/(Hypotenuse) \\\\Sine\ 45 = (w)/(3√(2)) \\\\Recall\\\\Sine 45 = (1)/(√(2)) \\\\Thus,\ we have:\\\\(1)/(√(2)) = (w)/(3√(2))\\\\Cross\ multitply\\\\w\ * √(2) = 3√(2)\\\\Divided both sides\ by √(2)\\\\w = ( 3√(2))/(√(2)) \\\\w = 3\ mm`