A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 31. From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 34. How high (in feet) is the mountain?

5507.79 feet

Step-by-step explanation:

To find the height of the mountain, we can draw triangles as in the image attached.

Let's call the height of the mountain 'h', and the distance from the first point (31 degrees) to the mountain 'x'.

Then, we can use the tangent relation of the angles:

tan(34) = h/x

tan(31) = h/(x+1000)

tan(31) is equal to 0.6009, and tan(34) is equal to 0.6745, so:

h/x = 0.6745 -> x = h/0.6745

using this value of x in the second equation:

h/(x+1000) = 0.6009

h/(h/0.6745 + 1000) = 0.6009

h = 0.6009 * (h/0.6745 + 1000)

h = 0.8909*h + 600.9

0.1091h = 600.9

h = 600.9 / 0.1091 = 5507.79 feet

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.

45

step-by-step explanation:

to find a percentage, add a decimal in front and multiply it by the other number.

.25 times 180= 45