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Solve problem using Trig?
While flying at an altitude of 1.5 km, a plane measures angles of depression to opposite ends of a large crater, as shown. Find the width of the crater, to the nearest tenth of a kilometer.
2 Answers
- llafferLv 72 years agoFavorite Answer
The lines make two right triangles. The angles near the plane can be found by subtracting the outer angle on each one by 90:
90 - 68 = 22 and 90 - 56 = 34
We know the height of both triangles but neither of the bases.
We can use tangents to find the length of the bases then add them together to get the total width of the crater:
tan() = opp/adj
tan(22) = x/1.5 and tan(56) = y/1.5
x = 1.5 tan(22) and y = 1.5 tan(56)
x = 0.6060 and y = 2.2238 (rounded to 4DP)
Add them together then round to 1DP:
0.6060 + 2.2238 = 2.8298
Rounded to 1DP, the width of the crater is 2.8 km.
