1. A woman wishing to know the height of a mountain measures the angle of elevation of the mountaintop as 10.4°. After walking 0.82 km closer to the mountain on level ground, she finds the angle to be 16.7°. Find the height of the mountain.

2. One cubic meter (1.00 m3) of aluminum has a mass of 2.70E+3 kg, and 1.00 m3 of gold has a mass of 1.93E+4 kg. Find the radius of an aluminum sphere whose mass is the same as that of an gold sphere of radius 1.44 cm.

3. A aerialist on a high platform holds on to a trapeze attached to a support by a 7.9 m cord. Just before he jumps off the platform, the cord makes an angle α of 38.2° with the vertical. He jumps, swings down, then back up, releasing the trapeze at the instant it is 0.52 m below its initial height. Calculate the angle θ that the trapeze cord makes with the vertical at this instant. (Enter the units of degrees as "deg")