Answer:
the rate at which the area of the triangle is increasing is [tex]1.2m^{2}/s[/tex]
Explanation:
The area A of the triangle is given by:
A = (1/2)bh
Where b is the base of the triangle and h is the height of the triangle. if we know 2 sides of the triangle, we can define b and h using the attached image as:
b = 10 m
h = 8 sen(x)
Where x is the angle between the sides of fixed length. So the Area of the triangle is:
A = (1/2)(10)(8*sen(x))= 40*sen(x)
Then, if we derive the equation of the area with respect to the time, we get:
[tex]\frac{dA}{dt} =40cos(x)\frac{dx}{dt}[/tex]
Where [tex]\frac{dx}{dt}[/tex] is the rate of the increasing angle.
So, if we replace this by 0.06 rad/s, we get:
[tex]\frac{dA}{dt} =40cos(x)(0.06)[/tex]
[tex]\frac{dA}{dt} =2.4cos(x)[/tex]
So, if x is equal to π/3, the rate at which the area of the triangle is increasing is:
[tex]\frac{dA}{dt}[/tex]=2.4cos(π/3)
[tex]\frac{dA}{dt} =1.2m^2/s[/tex]
