Question

NOTE: The picture is NOT drawn to scale. Ancient alien theorists manning two radar stations located b = 68 km apart both detect a UFO located between them. The angle of elevation measured by the first station (A) is a = 87.4 and the angle of elevation measured by the second station (C) is y = 84.4°

Answer 1

To find the distance between UFP and A, we need to calculate c.

Now, remember that the sum of the 3 internal angles of a triangle is equal to 180°.

So find angle B

`\beta=180°-87.4°-84.4°`
`\beta=8.2°`

Now with the law of sines calculate c:

`(b)/(sin\beta)=(c)/(\sin\gamma)`
`(68)/(sin(8.2°))=(c)/(\sin(84.4°))`
`c=(68*\sin(84.4°))/(\sin(8.2°))`
`c=474.49\text{ km}`

So the distance from A is 474.49 km

Now use this triangle to find h

You know the hypotenuse, which is equal to c=474.49km

`\sin\alpha=(h)/(c)`
`h=\sin\alpha *c`
`h=\sin(87.4°)*474.49`
`h=474\text{ km}`