A bridge across a valley is 150 m in length. The valley walls make angles of 60 degrees & 54 degrees with the bridge that spans it. How deep is the valley, to the nearest metre

Question

A bridge across a valley is 150 m in length. The valley walls make angles of  60 degrees & 54 degrees with the bridge that spans it. How deep is the valley, to the nearest metre

jim_thompson5910 · Answer

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jim_thompson5910 · Answer

you first need to find the missing angle

180 - (60 + 54) = 66 degrees

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jim_thompson5910 · Answer

then you use this to find either x or y (by using the law of sines)

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jim_thompson5910 · Answer

after you have 2 sides, and an included angle between them, you can use them in the formula

A = (1/2)*b*c*sin(theta)

A = area of the triangle
b = side 1
c = side 2
theta = angle between side 1 and side 2

jim_thompson5910 · Answer

finally, when you figure out the area, you can use it to solve for h in 

A = (b*h)/2

waheguru · Answer

So, I did it a different way. I split the triangle into two triangles and then I isolated how long ewach triangle would be then I found the depth but I was not getting the right answer

jim_thompson5910 · Answer

try following this method

waheguru · Answer

Sir, I posted tjis question in the history section my mistake can you please take a look here http://openstudy.com/study#/updates/51ad302ce4b06ee3ee25b694