Question

To find the distance between two radar installations a UFO calculates the distance to installation A to be 119 mi, the distance to installation C to be a = 77 mi, and the angle between them 6 = 34.6°. Find the distance between the installations.

Answer 1

Distance to A= 119mi

Disy¿tance to C=77mi

angle=34.6°

We have to find h, the angle that curts h will be half of 34.6, is a bisector

Using trigonometric to find h:

`Cos(\theta)=(c.a)/(119mi)=(h)/(119mi)`

Isolating h:

`\begin{gathered} cos((34.6)/(2))*119mi=h \\ \\ h=113.61 \end{gathered}`

Using the Pythagorean theorem we calculate x:

`\begin{gathered} 119^2=h^2+x^2 \\ x=\sqrt[\placeholder{⬚}]{119^2-h^2}=\sqrt[\placeholder{⬚}]{119^2-113.6^2}=35.4 \end{gathered}`

Now, we will use tan function:

`\begin{gathered} tan\theta=(b-x)/(h) \\ \\ h*tan\theta=b-x \\ \\ b=h*tan\theta+x=113.61*tan((34.6)/(2))+35.4=70.78 \end{gathered}`

The answer is: 70.78 mi.