From a certain point, the angle of elevation to the top of a church steeple is 10 degrees. At a point 100 m closer to the steeple, the angle of elevation is 20 degrees. Calculate the height of the church.
the answer i got (from using the sin/cos laws) was 34.21 m. can anyone confirm this for me? though my answer probably is wrong anyway . . .
thank you very much!
2007-09-14 16:53:14 · 11 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
oh wow, this is so much simpler than i thought. i don't get why i wrote down so many equations. oh well, thanks a lot!
2007-09-14 17:21:30 · update #1
another one (sorry about this):
from a certain point, the angle of elevation of the top of the tower is 65 degrees. from a point 56.6 m closer, the angle of elevation of the top of the tower is 70 degreese. calculate its height.
my answer is 114 m. please confirm?
2007-09-14 17:25:40 · update #2
h is height of steeple.
x is horizontal distance from foot of tower
as is (100 + x)
tan 10° = h / (100 + x)
h = tan10° (100 + x)
tan 20° = h / x
h = tan 20° x
tan 10° (100 + x) = tan 20° (x)
0 . 176 (100 + x) = 0 . 364 x
17.6 + 0.176 x = 0.364 x
0 . 188 x = 17.6
x = 93.6
tan 10° = h / 193.6
h = 193.6 tan 10°
h = 34.1 m
Height of steeple = 34.1 m
2007-09-18 07:23:46 · answer #1 · answered by Como 7 · 1⤊ 0⤋
It sounds reasonable, but from significant figures, the result should be 34.2 m. The result is 100*sin 20. If you set-up a diagram of the situation, the right triangle with the 10 degree elevation is a 10-80-90 triangle, while the right triangle with the 20 degree elevation is a 20-70-90 triangle. These leave a third triangle, which is a 10-160-10 triangle, the 160 degree angle being the supplement of the 20 degree angle of elevation. Thus you have an isoceles triangle with the equal sides being 100 meter, one of which is the hypotenuse of the 20-70-90 triangle.
2007-09-15 00:08:44 · answer #2 · answered by cattbarf 7 · 1⤊ 0⤋
We can't draw here so the explanation can't be very well.
According to your question,we have two triangles.
In the right triangle with angle '20' , the hypotenuse is 100m because the other triangle is isosceles with angles(10,10,160).
Let the height of the church be 'y' m.So:
sin(20) = y/100
y = sin(20) x 100
y = 34.20201
Our answers are approximately the same.Do you satisfy?
2007-09-15 00:18:22 · answer #3 · answered by Krait 2 · 1⤊ 0⤋
Your answer is right, 34.2 meters.
The law of sines shows that the hypotenuse of the inner triangle is 100 meters. From there I just used the definition of the sine.
y = hyp * sin(angle)
y = 100 * sin(20)
y = 34.2
2007-09-15 00:35:27 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Depends on what tables you use for the trig function -
tan (angle) I got 34.19 meters. So I think you are OK.
2007-09-15 00:12:59 · answer #5 · answered by stvenryn 4 · 1⤊ 0⤋
That's the answer I got. If we both got it wrong, we made the same mistake...so I believe we are correct.
2007-09-14 23:57:15 · answer #6 · answered by Big Will 2 · 1⤊ 0⤋
I got 38.72, but let's see what the rest say and go with the majority.
2007-09-14 23:58:08 · answer #7 · answered by Sheris_Sweet 3 · 1⤊ 0⤋
Thats about what I got with drafting program.
2007-09-15 00:24:53 · answer #8 · answered by Mike1942f 7 · 1⤊ 0⤋
I got the same
2007-09-15 00:11:28 · answer #9 · answered by charonnisis 3 · 1⤊ 0⤋
LOL lazy girl! I cant even with my own problems hehe
but u have to use trigonometry. ok ok I know that u knew it, lol. good luck!
2007-09-15 11:08:29 · answer #10 · answered by ~♣Miss Barcelona♣~ 6 · 0⤊ 1⤋