a difficult question,.....?

Question

often it is possible to make measurements directly, as in case of determining th eelevation of a mountain peak. describe how the law of sines and/or cosines can help with such measurements....

Answer 1

You need a basic understanding of trig. Sine of an angle is simply the length of the side opposite of the angle of a right triangle divided by the hypotenuse. The cosine of an angle is the length of the side adjacent to the angle of a right triangle divided by the hypotenuse.

Surveyors find rises in elevation by measuring the angle with a transit and measuring the distance to the object to get the height. They multiply the sine of the angle times the distance and get the height.

If its too far away, you can move to another location and repeat. use the concept of similar triangles to find the answer.

Answer 2

Imagine you are on flat ground. You can find the angle of elevation from your location to the mountain. Then you can move closer to the mountain and take another angle measurement. From 2 angles and the distance from one location to the other, you can measure the mountain elevation with respect to your location. In fact, with this you only need the basic sin and cosine definitions.

Answer 3

Essentially, to get the height of a mountain, you can measure two elevation angles at two points on a horizontal line towards to the mountain.

Let the two elevation angles be A and B at point A and point B, and the distance between A and B is d. You can find the height by
height = d/[1/tan(A) - 1/tan(B)], if A < B.

Answer 4

If you can measure the angle between the peak and the horizen at a known distance, then you can calculate the height with the sine and cosine of the angle.

Answer 5

LOVE your avatar:)