# Trig derivative applications

#### spoc21

Hi,

I'm having trouble with the following two questions which are applications of trig derivatives:

1) A rocket is moving into the air with a height function given by $$\displaystyle h(t) = 200t^2$$. A camera located 150 m away from the launch site is filming the launch. How fast must the angle of the camera be changing with respect to the horizontal 4 seconds after lift off?

2) The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is $$\displaystyle 100 cm^2?$$

I'm very confused with the two question
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#### skeeter

MHF Helper
Hi,

I'm having trouble with the following two questions which are applications of trig derivatives:

1) A rocket is moving into the air with a height function given by $$\displaystyle h(t) = 200t^2$$. A camera located 150 m away from the launch site is filming the launch. How fast must the angle of the camera be changing with respect to the horizontal 4 seconds after lift off?

2) The base of an isosceles triangle is 20 cm and the altitude is increasing at the rate of 1 cm/min. At what rate is the base angle increasing when the area is $$\displaystyle 100 cm^2?$$
1) let $$\displaystyle \theta$$ = camera angle

$$\displaystyle \tan{\theta} = \frac{200t^2}{150}$$

take the time derivative and determine the value of $$\displaystyle \frac{d\theta}{dt}$$ when $$\displaystyle t = 4$$

2) let $$\displaystyle \theta$$ = base angle

$$\displaystyle h$$ = altitude

$$\displaystyle \tan{\theta} = \frac{h}{10}$$

same drill ... take the time derivative and determine $$\displaystyle \frac{d\theta}{dt}$$ when $$\displaystyle A = 100$$

• spoc21