Question

A woman measures the angle of elevation of a mountaintop as $12.0^{\circ}$. After walking $1.00 \mathrm{~km}$ closer to the mountain on level ground, she finds the angle to be $14.0^{\circ} .$ (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. (c) Using the labeled picture and the tangent function, write two trigonometric equations relating the two sclected variables. (d) Find the height $y$ of the mountain by first solving one equation for $x$ and substituting the result into the other equation.

          A woman measures the angle of elevation of a mountaintop as $12.0^{\circ}$. After walking $1.00 \mathrm{~km}$ closer to the mountain on level ground, she finds the angle to be $14.0^{\circ} .$ (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. (c) Using the labeled picture and the tangent function, write two trigonometric equations relating the two sclected variables. (d) Find the height $y$ of the mountain by first solving one equation for $x$ and substituting the result into the other equation.

Added by David M.

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