Question

two adjacent sides of a parallelogram are 29 and 37, respectively. the angle between these two sides is 65°. find the length of c. round to the nearest tenth.

Explanation:

Step1: Identify applicable law

We use the Law of Cosines: for a triangle with sides $x,y$ and included angle $\theta$, the third side $z$ is $z^2=x^2+y^2-2xy\cos\theta$.

Step2: Substitute given values

Here $x=29$, $y=37$, $\theta=65^\circ$.
$$c^2=29^2+37^2-2(29)(37)\cos(65^\circ)$$

Step3: Calculate each term

$29^2=841$, $37^2=1369$, $2(29)(37)=2146$, $\cos(65^\circ)\approx0.4226$
$$c^2=841+1369-2146\times0.4226$$

Step4: Compute final value

$841+1369=2210$, $2146\times0.4226\approx906.9$
$$c^2=2210-906.9=1303.1$$
$$c=\sqrt{1303.1}\approx34.9$$

Answer:

34.9'