Trig word problem help please !!!?

Question

From two tracking stations A and B, 350 km apart, a ufo is is
sighted at C above AB, making angle CAB=32degrees
and angle CBA=54 degrees. Find the height of the UFO.

what is the easiest way this can be solved

Answer 1

draw the triangle and draw the height of the UFO; this is the unknown value, x. since you drew this as the height, this divides the base of 350 and forms ninety degree angles on either sides.

solve for either side (x) of the original triangle by the law of sines:
(remember that the three angles of a triangle sum to 180)

sineA/a = sineB/b

where A,B are the angles, and a,b are the respective opposite sides:

sine94/350 = sine54/x
x=283.85 -> this is side CA

Choose the smaller triangle that forms (I chose the 32 degree triangle).
Using the law of sines,

sine90/283.85 = sine32/x

x = 150.41 km.

Answer 2

This is a classic one-side two-angle triangle problem. The first thing I always do is a rough sketch of the situation, with the known information filled in.

Use the first formula in the link below and you should be able to come up with the remaining measurements of the triangle:
ACB = 94 degrees
AC = 283.8 km
BC = 185.9 km

Now you can draw a line straight down from the UFO (C) to the ground (AB). This creates two new right triangles. Now you can just use the sine function to determine the height of the UFO to be:
Height = 150.4 km

Answer 3

Angle C = 94°
350 / sin 94° = CB / sin 32°
CB = (sin 32°) (350) / sin (94°)
CB = 186 km
h = 186 sin 54°
h = 150 km ( to nearest km)