# Math Help - Trig derivative applications

1. ## Trig derivative applications

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 $h(t) = 200t^2$. 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 $100 cm^2?$

I'm very confused with the two question
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Thanks

2. Originally Posted by 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 $h(t) = 200t^2$. 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 $100 cm^2?$

1) let $\theta$ = camera angle

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

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

2) let $\theta$ = base angle

$h$ = altitude

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

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