Question

NOTE: The picture is NOT drawn to scale. To find the distance between two radar installations a UFO calculates the distance to installation A to be c = 88 km, the distance to installation C to be a = 76 km, and the angle between them 8 = 40.8°. Find the distance between the installations.Distance between the installations=Enter your answer as a number, your answer should be accurate to 2 decimal places.

Answer 1

The Law of the Cosines is used when two sides and the angle between them are known in a given triangle.

Let a and c two known sides of a triangle, and B the angle included, thus, the unknown side b is calculated as:

`b^2=a^2+c^2-2ac\cos B`

Substituting the given values a = 76 km, c = 88 km, B = 40.8°:

`b^2=76^2+88^2-2(76)(88)\cos40.8\~`

Calculating:

`\begin{gathered} b^2=3394.4341 \\ \\ b=√(3394.4341) \\ \\ b=58.26 \end{gathered}`

Distance between the installations: 58.26 Km