The heighthof the right triangle shown is increasing at a rate of 1 unit/s. Find the rate at which θ (in rad/s)is changing when h= 8

Question

Base is 6 units. that is all given. (right triangle)

Answer 1

tanθ = h/6

sec²θ(dθ/dt) = (1/6)(dh/dt)

6² + h² = c², where c is the length of the hypotenuse

So, when h = 8, 6² + 8² = c². Therefore, c = 10.

Thus, secθ = 1/cosθ = 1/(6/10) = 5/3

So, (5/3)²(dθ/dt) = (1/6)(1). Therefore, dθ/dt = (1/6)(9/25) = 3/50 radians/sec