A woman measures the angle of elevation of a mountaintop as 12.0°. After walking 0.80 km closer to the mountain on level ground, she finds the angle to be 14.0°
(a) Draw a picture of the problem, neglecting the height of the woman's eyes above the ground. Hint: Use two triangles.
(b) Select variable names for the mountain height (suggestion: y) and the woman's original distance from the mountain (suggestion: x) and label the picture. (Do this on paper. Your instructor may ask you to turn in this work.)
(c) Using the labeled picture and the tangent function, write two trigonometric equations relating the two selected variables. (Do this on paper. Your instructor may ask you to turn in this work.)
(d) Find the height y of the mountain by first solving one equation for x and substituting the result into the other equation.
The Attempt at a Solution
My two beginning equations are:
1. tan 12 = y/.8
2. tan 14 = y/x
The solution to equation 1 is .17
It seems to me that I no longer need to use two tangent equations as the problem suggests. I now know enough information for the following equation.
3. sin 14 = y/.17
Solution = .04km for the mountain height
I am way off the answer (which I know to be 1.15km)
What is wrong with my approach to the problem?
How do I substitute one equation into the other if I approach the problem in the suggested fashion?