Pre-calculus word problem!

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sweetsyd101

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Okay, so here's the problem.

Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 25 degrees and 24'. He then drives 1 mile (1 mile=5280 ft) more and measures the angle of elevation to be 34 degrees and 40'. Find the height of the mountain to the nearest foot.

I'm not allowed to use law of sines, so i have to solve it algebraically.

i've figured it out up to this point:

x/y = tan(25° 24')

x/(y+ 5280) = tan(34° 40')

but then i run into a little bit of a problem...i can't figure it out from there. i know you use the problems together and get them in terms of either x or y, but i don't know which one...i'm sort of terrible at math.
 
Be sure your calculator is set to degrees. Then find out what tan(25+24/60) is. I'll let that be represented by A. Then find out what tan (34+40/60) is. I'll let that be represented by B.
Now you have two equations in two unknowns.
 
sweetsyd101 said:
Okay, so here's the problem.

Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 25 degrees and 24'. He then drives 1 mile (1 mile=5280 ft) more and measures the angle of elevation to be 34 degrees and 40'. Find the height of the mountain to the nearest foot.

I'm not allowed to use law of sines, so i have to solve it algebraically.

i've figured it out up to this point:

x/y = tan(25° 24')

x/(y+ 5280) = tan(34° 40')<--------shouldn't the denominator be (y - 5280)? The second observation point is 5280 feet NEARER the mountain

but then i run into a little bit of a problem...i can't figure it out from there. i know you use the problems together and get them in terms of either x or y, but i don't know which one...i'm sort of terrible at math.
Click to expand...
 
sweetsyd101 said:
i've figured it out up to this point:

x/y = tan(25° 24')

x/(y+ 5280) = tan(34° 40')
Click to expand...


Why do you force people to guess at what your symbols x and y represent?

From your statement that the tangent of the first measured-angle is x/y, I deduce that you've made the following choices.

x = the height of the mountain (in feet)

y = the horizontal distance from Bob's first stop to a point directly below the tip of the mountain (in feet)

Write this down!

Your mistake is writing y + 5280 for the base of the second triangle. It is y - 5280.

Also, the two tangent expressions that you wrote are constants. Do you have a scientific calculator? 8-) Finding these two constants is the second step.

0.4748 = x/y

0.6915 = x/(y - 5280)

Journey onward with your algebraic solution to this system of two equation in x and y!

Cheers ~ Mark

 
Sorry about not writing what x and y meant, i had it labeled on my picture, so i didn't think about writing it out.

the + instead of minus was a typo, my mistake!

anyways, after i worked it out, i got 8000 to be the height...is that right?

thanks everyone for helping me out!!
 
sweetsyd101 said:
… got 8000 to be the height … is that right? …

I would not give full credit for that answer.

"To the nearest foot, the height of the mountain is 8,000 feet." 8-)
Click to expand...


Next time you ask for long-distance help, try to remember that other people cannot see your papers.

Also, for sloppy typists, this site has a [Preview] button for proofreading posts before submitting them.

 
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