Shortly after takeoff, an airplane is climbing 250 feet for every 1,000 feet it travels. Estimate the airplane's climb angle while this is happening.
Answer
\( \boxed{14.04} \) is the airplane's climb angle.
Step 1 ：Given an airplane climbing 250 feet for every 1,000 feet it travels, we can use the tangent function to find the climb angle. In a right triangle, the tangent of an angle is the ratio of the opposite side (the climb) to the adjacent side (the horizontal distance traveled). So, we have: \( \tan(\theta) = \frac{250}{1000} \)
Step 2 ：To find the angle in degrees, we can use the arctangent function (atan) and then convert it to degrees: \( \theta = \arctan(\frac{250}{1000}) \times \frac{180}{\pi} \approx 14.04 \) degrees
Step 3 ：\( \boxed{14.04} \) is the airplane's climb angle.
