A100ft. ladder rests on top of a hook and ladder truck with its base 11 feet from the ground. when the angle of evelation of the ladder is 81 degrees, how high up the building will the ladder reach?

Using the slope concept, it is found that the ladder reaches a height of 69.45 feet.

The slope is given by the vertical change divided by the horizontal change.

It's also the tangent of the angle of depression.

In this problem:

Hence:

The ladder reaches a height of 69.45 feet.

More can be learned about the slope concept at link

  109.77 ft

Step-by-step explanation:

It can be useful to draw a diagram. It doesn't have to be fancy or to scale. It just needs to illustrate the relationships given in the problem statement.

The height up the building will be the length of the side of the right triangle opposite the angle plus the 11 foot height of the ladder base above the ground.

The mnemonic SOH CAH TOA reminds you of the relationship between the opposite side and the hypotenuse in a triangle:

  Sin = Opposite/Hypotenuse

Then the length of the opposite side is found from ...

  hypotenuse × sin(81°) = opposite

  (100 ft) × 0.987688 = opposite ≈ 98.77 ft

Then the height of the end of the ladder is ...

... 98.77 ft + 11 ft = 109.77 ft