Question

URGENT PLEASE HELP!!!! GIVING BRAINLIEST!! If you answer this correctly ill answer some of your questions you have posted! (39pts)

Answer 1

Answer:

So the trench is 37.5 feet wide

Step-by-step explanation:

The trench with telescope is 18 feet higher than the other.

The height of telescope is 4.5 feet.

Total height = 18 + 4.5 = 22.5

Now, we can see in the figure that the distances between telescope and the opposite trench, the height and width makes a right angled triangle.

So, perpendicular = total height = 22.5

base = wideness of the trench

We know,

Tan 31 = p/b

tan 31 = 22.5/b

b = 22.5 / 0.6

b = 37.5

Answer 2

Answer:

The first transit on one side of the trench is 18 ft higher than the other side of the trench. The transit is set at 4.5 above ground, therefore the transit lens is 18' + 4.5' = 22.5' above the location on the other side of the trench. The angle of depression is the angle formed by the horizontal and the line of sight to the other side and it is given as 31°. This forms a right angle triangle with height of 22.5' and an interior angle of 31°, Then

tan( 31°) = Height / base, with the base representing the width of the trench

base = Height / tan(31°) = 22.5' / tan(31°) = 37.45' is the width of the trench