The people of Bridgetown wanted to build a bridge across a nearby river. Since they were poor swimmers, their
master Trigonomos agreed to measure the width of the river without actually crossing it.
Trigonomos spotted a tree across the river and marked the spot directly across from it. Then he walked to
another point 10 meters down the river and found that the angle between his side of the river and the line
connecting him to the tree was 40°.
What is the width of the river?
Round your final answer to the nearest hundredth.
meters

  8.39 meters

Step-by-step explanation:

The angle is opposite the side of interest of the right triangle representing the geometry. The adjacent side is known, so the tangent function can be useful.

  Tan = Opposite/Adjacent

  tan(40°) = width/(10 m) . . . . . filling in given values

  (10 m)·tan(40°) = width ≈ 8.390996 m ≈ 8.39 m

The width of the river is about 8.39 meters.

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)