A forest ranger spots a forest fire from the top of a lookout tower. The tower is 150m tall, and the angle of depression to the fire is 10 degrees. About how far is the fire from the foot of the tower? Round to the nearest meter.
A. 148m
B. 753m
C. 863m
D. 851m
I tried to use the tangent but it kept on iving me 26.4 or something like that and I couldn't figure out what I was doing wrong even though this simple trigonometry is usually pretty easy for me.
2006-12-24 09:06:04 · 10 answers · asked by emimi 2 in Science & Mathematics ➔ Mathematics
The answer is D. 851
When you drew you triangle you most likely used the standard position, however with an angle of depression you would use the fourth quadrant. x would then be the adjacent side and 150 being the opposite side. Then use the tangent to find the solution.
2006-12-24 09:26:40 · answer #1 · answered by tval_friedly 2 · 4⤊ 0⤋
tan θ = opposite side / adjacent side
Let x be the distance to the fire from the foot of the tower.
tan 10° = 150/x
x = 150/tan 10° = 851 m
The answer is D. 851 m
2006-12-24 16:01:43 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
If the angle of depression is 10 degrees, that means that the height is 150 m, the length is x, and 10 degrees is the angle such that tan(10) = 150 / x, so x = 150 / tan(10) = 851 m, so D.
The problem is that you took 150*tan(10) instead of 150 / tan(10).
2006-12-24 09:11:21 · answer #3 · answered by DavidK93 7 · 5⤊ 0⤋
Choice D
tan 10=150/x
x=150/tan 10
x=850.69...
2006-12-24 10:45:51 · answer #4 · answered by abcde12345 4 · 2⤊ 0⤋
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
2016-05-23 04:32:02 · answer #5 · answered by ? 4 · 0⤊ 0⤋
angle of depression is 10° side opposite=150 m
side adjacent is the distance.
tan 10°=150/d
d=150/tan 10°=851 m
2006-12-24 09:11:10 · answer #6 · answered by mu_do_in 3 · 4⤊ 0⤋
150/x = tan 10 degrees
x = 150 / tan 10 degrees
x= 150/0.17633 = 850.7 m = 851 m
2006-12-24 10:10:36 · answer #7 · answered by ironduke8159 7 · 2⤊ 0⤋
x=the distance from the fire and the bottom of the tower.
tan(10)=150/x
Multiply x from both sides:
tan(10)x=150
Divide tan(10) from both sides:
x=150/tan(10)≈851
The answer is D) 851m.
I hope that helps!
2006-12-24 10:01:17 · answer #8 · answered by Anonymous · 3⤊ 0⤋
x = adjacent side.
tan(10deg) = 150/x
x = tan(10)*150 = 26.45 <-- your answer.
see what happened?
the actual solution is:
x = [150]/[tan(10)] = 850.69 ~= 851.
2006-12-24 09:14:39 · answer #9 · answered by John C 4 · 4⤊ 0⤋
D. tan10=150/x, x=150/tan10, x=851m.
2006-12-24 13:32:06 · answer #10 · answered by Deano 7 · 1⤊ 0⤋