Answer:
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
