Posted by **christina** on Sunday, October 20, 2013 at 11:35pm.

Two sides of a triangle have lengths 8 m and 24 m. The angle between them is increasing at a rate of 0.05 rad/s. Find the rate at which the area of the triangle is changing when the angle between the sides of fixed length is 135°. Round your answer to two decimal places.

So it would be

Using the formula:

area = (1/2) ab sinŲ , where a and b are the sides and Ų is the contained angle

A = (1/2)(8*24)sinŲ

A = 96 sinŲ

dA/dt = 96cosŲ dŲ/dt

given: dŲ/dt = .05

dA /dt = 96(cos(135)(.05) = -3.40

I keep getting it wrong?

- math -
**Reiny**, Sunday, October 20, 2013 at 11:53pm
Who says it is wrong?

I get the same result

Make a sketch with the arms at 135° ........ (90+45)

if you increase the angle , you will see that the area is actually getting smaller, (the lines eventually will become a straight line, at which point the area is zero)

at Ų = 134.99° , A = 67.894097

at Ų = 135.01° , A = 67.87040..

notice that the area has decreased slightly for that small increase in the angle

- math -
**christina**, Sunday, October 20, 2013 at 11:57pm
My online homework says it is wrong. I tried it without the negative sign too

- math -
**Anonymous**, Monday, October 21, 2013 at 12:26am
-4.78

- math -
**Kuai**, Monday, October 21, 2013 at 12:30am
dA /dt = 96(cos(135)(.05) = -3.39

## Answer this Question

## Related Questions

- math - Two sides of a triangle have lengths 15 m and 18 m. The angle between ...
- Math - The two sides of a isosceles triangle have a fixed lenght of 14 cm. The ...
- Math - The two sides of a isosceles triangle have a fixed lenght of 14 cm. The ...
- Math - The two sides of a isosceles triangle have a fixed lenght of 14 cm. The ...
- Math - The two sides of a isosceles triangle have a fixed lenght of 14 cm. The ...
- Calculus - 1) Find correct to six decimal places root of the equation cos(x)= x...
- AP CALC. AB - Two sides of a triangle have lengths 13 m and 17 m. The angle ...
- isosceles triangle - An isosceles triangle is a triangle that has two equal ...
- calculus - the sides of an equilateral triangle are increasing at a rate of 27 ...
- pre-calculus - suppose a triangle has two sides of lengths a and b. if the angle...

More Related Questions