Answer:
[tex]a =\frac{\sqrt 3}{2}[/tex] mi
[tex]b =\frac{1}{2}[/tex] 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
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
So, we have:
[tex]\sin(60) = \frac{a}{c}[/tex]
[tex]\sin(30) = \frac{b}{c}[/tex]
Where
[tex]c = 1[/tex]
So, we have:
[tex]\sin(60) = \frac{a}{c} =\frac{a}{1}[/tex]
[tex]\sin(60) = a[/tex]
[tex]a = \sin(60)[/tex]
In radical form:
[tex]\sin(60) = \frac{\sqrt 3}{2}[/tex]
Hence:
[tex]a =\frac{\sqrt 3}{2}[/tex]
[tex]\sin(30) = \frac{b}{c}[/tex]
[tex]\sin(30) = \frac{b}{1}[/tex]
[tex]\sin(30) = b[/tex]
Rewrite as:
[tex]b =\sin(30)[/tex]
In radical form:
[tex]\sin(30) = \frac{1}{2}[/tex]
Hence:
[tex]b =\frac{1}{2}[/tex]
