SOLUTION: Two people at opposite ends of a bridge see a boat under the bridge at angles of 32 degrees and 55 degree each. Find the height of the bridge if it is 200m long.
I do have a pho
Algebra.Com
Question 1151496: Two people at opposite ends of a bridge see a boat under the bridge at angles of 32 degrees and 55 degree each. Find the height of the bridge if it is 200m long.
I do have a photo but not sure how to upload it.
thanks
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
x, the length along the bridge from the person at the 55 degree angle
h, the height from bridge to boat
.
.
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(Mistakes possible - not checked)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You can upload image attachments (at least I think you can) directly to the algebra.com website as you ask a question.
Alternatively, you can use image hosting sites such as imgur or similar to share the image. Those sites will allow you to provide a link to be able to show the image. Let me know if you need more details.
Despite the fact that there is no picture, your description seems to be enough for me to visualize what's going on.
Here is how I picture it.
Points A and B are the locations of the two people on the bridge. Point C is the boat's location. The image displayed here is being hosted by imgur.
Known info:
A = 32, B = 55
c = 200
From the two angles given, we can compute angle C as
C = 180-A-B
C = 180-32-55
C = 93
We can use the law of sines to get…
a/sin(A) = c/sin(C)
a/sin(32) = 200/sin(93)
a = sin(32)*(200/sin(93))
a = 106.12929936294 which is approximate
Now I'm going to add in the red height line of length h
Focus on triangle BCD. Use the sine ratio to isolate h.
sin(angle) = opposite/hypotenuse
sin(B) = h/a
h = a*sin(B)
h = 106.12929936294*sin(55)
h = 86.9360325321108
h = 86.94
The height of the bridge is roughly 86.94 meters.
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