4. Prior to their retirement from spaceflight, Space Shuttle Orbiters returned to Earth as gliders - really terrible gliders, as it turns out (the Space Shuttle was nicknamed the Flying Brick.) As the shuttle decends through the atmosphere to land on a runway, it drops vertically $3.4 \mathrm{~m}$ for every $10 \mathrm{~m}$ it flies forward.
(a) (5 points) Use trigonometry to figure out the angle below the horizontal (in degrees) of the Space Shuttle's trajectory.
\[
\tan \theta=\frac{3.4}{10}
\]
(b) (5 points) A commercial airliner approaches the runway along a trajectory tipped about $3^{\circ}$ below the horizontal. How many meters does it drop for every $10 \mathrm{~m}$ it flies forward?
Answer
\(h \approx \boxed{0.52}\)
Step 1 ：\(\tan \theta = \frac{3.4}{10}\)
Step 2 ：\(\theta = \arctan \left(\frac{3.4}{10}\right)\)
Step 3 ：\(\theta \approx \boxed{18.43^\circ}\)
Step 4 ：\(\tan 3^\circ = \frac{h}{10}\)
Step 5 ：\(h = 10 \tan 3^\circ\)
Step 6 ：\(h \approx \boxed{0.52}\)
