I don't know how good you are at drawing a 3D diagram.
Start with a NSEW grid and place A at the origin.
(I angled my North and East axes at about 60° to each other, but marked the angle at A as ∟ (90°)
Draw in MC, the meteor, where C is on the North axis.
We want MC, a vertical side in the rightangled triangle MAC , where C is the 90° angle and angle A = 70°
Mark position B on the East axis, so that AB = 30 miles
Joint BC and BM to have another right-angled triangle BMC, with angle C = 90°
From B, sketch another NORTH axis BD, so that BD || AC
We are told that angle DBC = 50° (N 50 W)
so in the right-angled triangle ABC, angle ABC = 90-50 = 40°
Now for our calculations:
In triangle ABC,
AC/AB = tan 40°
AC = ABtan40
AC= 30tan40°
in triangle MAC,
MC/AC = tan70
MC = ACtan70
= 30tan40tan70
= appr 69.2 miles
for the distance MA,
sin 70 = MC/MA
MA = MC/sin70 =73.6 miles
check my arithmetic
an observer at A looks due north and sees a meteor with an angle of elevation of 70 degrees. At the same instant, another observer 30 miles east of A seed the same meteor and approximates its position as N 50 degrees W but fails to note its angle of elevation. Find the height of meteor and its distance from A.
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