A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as θ1 = 11.6°. After walking d = 0.81 km closer to the mountain on level ground, she finds the angle to be θ2 = 13.7°. a. Draw a picture of the problem, neglecting the height of the woman's eyes above the ground. 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. (Dothis on paper. Your instructor may ask you to turn in thiswork.)d. Find the height y of the mountain by first solving one equation for x and substituting the result into the other equation.

a. In the attached image.

b. Height of the mountain: y

Original distance between the woman and mountain: x

c. tan(11.6) = y/x ; tan(13.7) = y/(x - 0.81)

d. The height of the mountain is 10.38m

Explanation:

a. In the attached image.

b. Variable Names:

The height of the mountain: y

The original distance between the woman and mountain: x

c. Trigonometric functions.

Using tan function of SOHCAHTOA trigonometric function:

For the woman's original position, Triangle ACD in the image,

tan(θ₁) = y/x

tan(11.6) = y/x ........... (1)

For the woman's second position, Triangle BCD in the image,

tan(θ₂) = y/(x - 0.81)

tan(13.7) = y/(x - 0.81) ....... (2)

d. To find y, solve for x in (1) and substitute into (2):

x = y/tan(11.6) (from 1)

x = [y/tan(13.7)] + 0.81 (from 2)

Fixing the value of x from (1) into the equation above:

y/tan(11.6) = [y/tan(13.7)] + 0.81

y/0.205 = [y/0.244] + 0.81

Multiplying through by 0.244 * 0.205

=> 0.244y = 0.205y + (0.81 * 0.244 * 0.205)

0.244y = 0.205y + 0.0405

0.244y - 0.205y = 0.0405

0.039y = 0.405

y = 10.38m

The height of the mountain is 10.38m