Question

The image shows a portion of a bridge supported by two vertical pillars built from the points B and C on the slope below. The length of the bridge between pillar B and pillar C is BLANK feet.

Answer 1

The length of the bridge between pillar B and pillar C is 56 feet.

Here's the answer from the plato.

Answer 2

In order to find the length of ?? (let's call this distance x), let's first find the value of Angle A.

The cosin of Angle A is Adjacent / Hypotenuse, or 40 / 50. Using this Info:
cos (A) = 40/50
cos (A) = .8

With this crucial piece of info, we can find the Total length of A-D (Point D being the point above C), by finding its relation to side AC (length of 50 + 70 =120 ft)
Cos (A) = adjacent / hypotenuse
Cos (A) = AD / (120) We know that cos (A) = .8
.8 = AD / (120) Multiply both sides by 120
96 = AD

We're almost there! Remember that we're trying the find x (?? in the diagram).

x + 40 = 96
x = 56 ft