Question

What are the lengths of sides a and b?​

Answer 1

`a =(\sqrt 3)/(2)` mi

`b =(1)/(2)` mi

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(60) = (a)/(c)`

`\sin(30) = (b)/(c)`

Where

`c = 1`

So, we have:

`\sin(60) = (a)/(c) =(a)/(1)`

`\sin(60) = a`

`a = \sin(60)`

In radical form:

`\sin(60) = (\sqrt 3)/(2)`

Hence:

`a =(\sqrt 3)/(2)`

`\sin(30) = (b)/(c)`

`\sin(30) = (b)/(1)`

`\sin(30) = b`

Rewrite as:

`b =\sin(30)`

In radical form:

`\sin(30) = (1)/(2)`

Hence:

`b =(1)/(2)`