11. Two support wires are fastened to the top of a satellite dish tower from points $A$ and $B$ on the ground, on either side of the tower. One wire is $18 \mathrm{~m}$ long, and the other wire is $12 \mathrm{~m}$ long. The angle of elevation of the longer wire to the top of the tower is $38^{\circ}$.
a) How tall is the satellite dish tower?
Answer
\(\boxed{\text{The satellite dish tower is approximately 11.08 meters tall}}\)
Step 1 ：Convert the angle of elevation from degrees to radians: \(38^\circ = 0.6632251157578453 \text{ radians}\)
Step 2 ：Use the sine function to find the height of the tower: \(\text{height} = 18 \times \sin(0.6632251157578453)\)
Step 3 ：Calculate the height: \(\text{height} = 11.081906555861849\)
Step 4 ：\(\boxed{\text{The satellite dish tower is approximately 11.08 meters tall}}\)
