The area A of a triangle is given by A = 1 2 a b sin θ , where a and b are the lengths of two sides and θ is the angle between these sides. Suppose that a = 5 , b = 10 , and θ = π / 3. (a) Find the rate at which A changes with respect to a if b and θ are held constant. (b) Find the rate at which A changes with respect to θ if a and b are held constant. (c) Find the rate at which b changes with respect to a if A and θ are held constant.
The area A of a triangle is given by A = 1 2 a b sin θ , where a and b are the lengths of two sides and θ is the angle between these sides. Suppose that a = 5 , b = 10 , and θ = π / 3. (a) Find the rate at which A changes with respect to a if b and θ are held constant. (b) Find the rate at which A changes with respect to θ if a and b are held constant. (c) Find the rate at which b changes with respect to a if A and θ are held constant.
The area A of a triangle is given by
A
=
1
2
a
b
sin
θ
,
where a and b are the lengths of two sides and
θ
is the angle between these sides. Suppose that
a
=
5
,
b
=
10
,
and
θ
=
π
/
3.
(a) Find the rate at which A changes with respect to a if b and
θ
are held constant.
(b) Find the rate at which A changes with respect to
θ
if a and b are held constant.
(c) Find the rate at which b changes with respect to a if A and
θ
are held constant.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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