Shari and Leo are standing 36 m apart and facing each other. If Shari looks upward, the angle of elevation of a hot air balloon in the sky is /4 radians and from Leo the angle of elevation is /3 radians. Calculate the height of the hot air balloon from the ground, to the nearest tenth of a metre.

1. Angle a lies in the second quadrant and angle b lies in the third quadrant such that cos a = -3/5 and tan b = 24/7 . Determine an exact value for a) cos(a +b) b) sin(a - b) c) sin 2a

2. A 15-m ladder leaning against a wall is in an unsafe position if it makes an angle of less than /12 radians with the wall. Use a compound angle formula to determine an exact expression for the minimum distance that the foot of the ladder can be placed from the wall so that the ladder is standing safely.