A woman measures the angle of elevation of a mountaintop as 12.0°. After walking 1.00 km closer to the mountain on level ground, she fi nds 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. (c) Using the labeled picture and the tangent function, write two trigonometric equations relating the two selected variables. (d) Find the height y of the mountain by fi rst solving one equation for x and substituting the result into the other equation.

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mauricioalessandrell mauricioalessandrell · Answer 1 · 2019-09-12T21:37:43+02:00

Answer:

The height of the mountain is 1.33 km.

Explanation:

a and b) See the attached figure for a description of the situation

c) For right triangles, this trigonometric rule applies:

tangent angle = opposite side / adjacent side

Then, in our problem:

tg 12º = y / x

tg 14º = y / (x-1)

d) using the first equation:

tg 12º = y / x

x * tg 12º = y

Replacing "y" for "x * tg 12º" in the second equation and solving for x:

tg 14º = (x * tg 12º) / (x-1)=

tg 14º * (x-1) = tg 12º * x

0.25 x -0.25 = 0.21 x

0.25 x - 0.21 x = 0.25

0.04 x = 0.25

x = 6.25

Then:

y = tg 12º * x

y = 6.25 * tg 12º = 1.33 km