Pre-Calculus help?!

Pre-College Issues High School Life
1

<p>Hey everybody. My teacher gave out a hard trigonometry problem and not many people understand it. If you can help me, or at least get me started, I would greatly appreciate it. I am not a math person at all! Honestly, at all. :)</p>

<p>Problem:</p>

<p>The pilot of a small private plan can look forward and see the control tower for a small airstrip. Beyond that is a large factory that is 3.7 miles from the airstrip. The angles of depression are 9.8 degrees and 3.3 degrees, respectively. Find the airplane's altitude, to the nearest foot. (Caution: miles vs. feet!) HINT: Write 2 equations, solve for the unknown variable, then use substitution to solve for a, the altitude.</p>

<p>Please private message me if you math whizzes can figure this out. I don't even know where to start. Thank you!</p>

2

<p>h/x=tan(9.8)
h/(x+3.7)=tan(3.3)
x is horizontal distance from plane to tower, h is height of airplane</p>

<p>x/(x+3.7)=tan(3.3)/tan(9.8), solve for x
plug x back into one of the first 2 equations and solve for h
convert h from miles to feet</p>

<p>I'm getting about 9789 feet.</p>

3

<p>Thank you so much! I appreciate it.</p>

4

<p>Sorry, the answer I gave was the horizontal distance. The altitude I'm getting is 1691 feet.</p>

5

<p>Thank you! You used the conversion factor of 5280 ft in one mile, right?</p>

6

<p>Yeah .</p>

7

<p>I feel so dumb. How do I solve for x? x/(x+3.7)=tan(3.3)/tan(9.8), right? Do we cross multiply? I'm having trouble isolating the x. :(</p>

8

<p>Do I need to be in degree mode on my calculator? Sorry for all the questions.</p>

9

<p>I dont know what mode you should be on, but if you put in radian mode, the answer is 2.524. If you do it in degree mode, then the answer is 1.854. And this is how you do it:
First, solve for tan(3.3)/tan(9.8), let's say the result come out to be the answer A
--> x/(x+3.7) = A
Multiply both sides by x+3.7, you got--> x = Ax + 3.7A
put x's to one side --> x - Ax = 3.7A
--> x(1-A) = 3.7A
--> x = 3.7A/(1-A)
Doesn't matter which code you choose, you still do it the same way.</p>

10

<p>Thanks! So, if I plug x back into the first equation, I'd have h/3.7A/1-A=tan(9.8), right?</p>

11

<p>If you plug x back into the original equation, everything is just canceled out.</p>

12

<p>Ahhh, I'm so confused. When you plug it back into the first equation, everything's canceled out? The answer is zero?</p>

13

<p>Maybe because it's on the computer, but I still can't see how we get the answer 1619. :(</p>

14

<p>In towerpumpkin's equation, I don't even see an A. How does that come in? I'm so lost and I feel like an idiot. lol</p>

15

<p>Since the angles are in degrees, you need to be in degree mode. To solve those two equations, divide one by the other, cross multiply, and then distribute everything out. It wont look very pretty. The answer you get from that should be in miles; convert that to feet.</p>

16

<p>ok forget A, it's just the answer you got when you plug in your calculator tan(3.3)/tan(9.8), which is 0.334. Then you follow the direction I showed above.
Notes: it is NOT an equation that you can find in your book. It's just a common way to solve a problem. I didn't use any formula in this problem, tell me if there's anything else you don't understand ^_^</p>