Asked by Brittani
A woman measures the angle of elevation from her current location to a mountaintop to be 12.0°. After walking 1.10 km closer to the mountain on level ground, she measures the angle again and finds it to be 14.0°. What is the height of the mountain?
Answers
Answered by
Henry
1. Draw a hor. line.
2. Draw a ver. line to the right-end of the hor. line and label it h for height.
3. From the left-end of the hor. line, draw a hypotenuse to the top of the ver. line. The angle it makes with the
hor. is 12o.
4. Draw a 2nd hyp. to the right of the first and label the distance between them X1 = 1.1 km. The remaining section
is X2.
Tan12 = h/(x1+x2) = h/(1.1+x2)
h = (1.1+x2)*Tan12
Tan14 = h/x2
h = x2*Tan14
x2*Tan14 = (1.1+x2)*Tan12
0.249x2 = 0.213x2 + 0.234
0.249x2-0.213x2 = 0.234
0.036x2 = 0.234
X2 = 6.5 km
h = X2*Tan14 = 6.5 * Tan14 = 1.62 km.
2. Draw a ver. line to the right-end of the hor. line and label it h for height.
3. From the left-end of the hor. line, draw a hypotenuse to the top of the ver. line. The angle it makes with the
hor. is 12o.
4. Draw a 2nd hyp. to the right of the first and label the distance between them X1 = 1.1 km. The remaining section
is X2.
Tan12 = h/(x1+x2) = h/(1.1+x2)
h = (1.1+x2)*Tan12
Tan14 = h/x2
h = x2*Tan14
x2*Tan14 = (1.1+x2)*Tan12
0.249x2 = 0.213x2 + 0.234
0.249x2-0.213x2 = 0.234
0.036x2 = 0.234
X2 = 6.5 km
h = X2*Tan14 = 6.5 * Tan14 = 1.62 km.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.