Question

What are the lengths of side a and b?​

Answer 1

`a =(\sqrt 2)/(2)` m

`b=(\sqrt 2)/(2)` m

Explanation:

Given

The attached triangle

Required

Find a and b

To do this, we make use of the following trigonometry ratio

`\sin(\theta) = (Opposite)/(Hypotenuse)`

So, we have:

`\sin(45) = (a)/(c)`

`\sin(45) = (b)/(c)`

Where

`c = 1`

So, we have:

`\sin(45) = (a)/(1)`

`\sin(45) = a`

Rewrite as:

`a =\sin(45)`

In radical form:

`\sin(45) =(\sqrt 2)/(2)`

So:

`a =(\sqrt 2)/(2)`

Similarly:

`\sin(45) = (b)/(c)`

`\sin(45) = (b)/(1)`

`\sin(45) = b`

Rewrite as:

`b = \sin(45)`

In radical form:

`\sin(45) =(\sqrt 2)/(2)`

So:

`b=(\sqrt 2)/(2)`