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

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

1 and 2

step-by-step explanation: