To solve this problem, we can use trigonometry. Specifically, the sine function is useful because we are dealing with a right triangle formed by the ladder, the building, and the ground.

The ladder is the hypotenuse of the triangle, and the vertical distance from the ground to the point where the ladder contacts the building is the side opposite the angle.

Formula:

We will use the sine function, which is defined as:

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Where:

• $\theta = 30^\circ 7'$ (which we need to convert to decimal degrees first)
• The hypotenuse = 38 feet (length of the ladder)

Step 1: Convert the angle to decimal form

30 degrees 7 prime means 30 degrees and 7 minutes. To convert minutes to decimal degrees:

$7' = \frac{7}{60} = 0.1167^\circ$

Thus, the angle $\theta = 30 + 0.1167 = 30.1167^\circ$.

Step 2: Use the sine formula

Now, we can apply the sine formula:

$\sin(30.1167^\circ) = \frac{\text{opposite}}{38}$

Solving for the opposite side (the height where the ladder contacts the building):

$\text{opposite} = 38 \times \sin(30.1167^\circ)$

Step 3: Calculate the height

Now, calculate the sine of 30.1167 degrees:

$\sin(30.1167^\circ) \approx 0.5009$

So,

$\text{opposite} = 38 \times 0.5009 \approx 19.05 \text{ feet}$

Conclusion:

The distance up the building where the ladder contacts is approximately 19.05 feet, which isn't listed as an answer choice. However, I suspect that either the angle or the answer choices might have been provided in a different context or there might be an oversight in the problem. Would you like me to verify or adjust anything further?