Question

You're lying on a beach. Some distance away, across level ground, is a tall coconut palm. As you watch, a monkey in that tree drops a coconut (from rest) onto hard ground below. The time elapsed from the moment he releases the coconut until it hits the pavement is three times as long as the time it takes for the sound of the impact to reach you. The angle (measured with respect to the ground) at which you are viewing the monkey when he drops the nut is 4.40degrees. Assuming the speed of sound is a constant 343m/sec, from what height did tha monkey drop the nut?

Answer 1

You have only one variable, H=height of the palm tree.
The distance, D can be expressed in terms of H through Dtan(4.4°)=H
since
H=v0T+(1/2)gT²
Time T for coconut to reach the ground from rest = sqrt(2H/g)

From:
"The time elapsed from the moment he releases the coconut until it hits the pavement is three times as long as the time it takes for the sound of the impact to reach you."
we form the equation:
T=3*D/Vs
where Vs=velocity of sound = 343 m/s
Solve for H.