Question

What are the lengths of sides a and b?​

Answer 1

Answer:

$a =\frac{\sqrt 3}{2}$ mi

$b =\frac{1}{2}$ mi

Step-by-step explanation:

Given

The attached triangle

Required

Find a and b

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

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

So, we have:

$\sin(60) = \frac{a}{c}$

$\sin(30) = \frac{b}{c}$

Where

$c = 1$

So, we have:

$\sin(60) = \frac{a}{c} =\frac{a}{1}$

$\sin(60) = a$

$a = \sin(60)$

In radical form:

$\sin(60) = \frac{\sqrt 3}{2}$

Hence:

$a =\frac{\sqrt 3}{2}$

$\sin(30) = \frac{b}{c}$

$\sin(30) = \frac{b}{1}$

$\sin(30) = b$

Rewrite as:

$b =\sin(30)$

In radical form:

$\sin(30) = \frac{1}{2}$

Hence:

$b =\frac{1}{2}$