Find the length of each segment with endpoints a and B. Select the exact answer (This means it is either an integer or in simplest radical form)

  183.7 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation between the hypotenuse and opposite side in a right triangle is ...

  Sin = Opposite/Hypotenuse

For the first observation, the angle is 45° and the length of the hypotenuse of the triangle is given as x. For the second observation, the opposite side (building height) is the same, the angle is 60°, and the hypotenuse is 150 ft.

We can multiply the above equation by "Hypotenuse" to get an expression for "Opposite".

  Opposite = Sin×Hypotenuse

For our two observations, this becomes ...

  sin(45°)·x = (building height) = sin(60°)·(150 ft)

Dividing by the coefficient of x, we have ...

  x = (150 ft)·sin(60°)/sin(45°) ≈ 183.7 ft