Trigonometric differentiation problem

matthewspj · #1 $Old$ 08-29-2008, 11:45 AM

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

Jhevon · #2 $Old$ 08-29-2008, 12:49 PM

Quote:

Originally Posted by matthewspj $View Post$

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

A is the area, h is the height, b is the length of the base and $\theta$ is the base angle.

recall that $A = \frac 12 bh$

this means, when A = 100, h = 10.

we are also told that $\frac {dh}{dt} = 1$ . b is constant at 20cm, and so $\frac {db}{dt} = 0$ , but we wont even have to worry about that.

draw your triangle, and bisect the base with a vertical line going through the top vertice. $\theta$ is the base angle and we form a right triangle with the opposite side to theta being h and the adjacent side being 10.

Thus we have $\sin \theta = \frac h{10}$

now differentiate implicitly and continue