The measure of , in degrees, is approximately 48.8. true or false

Using the Law of cosines in this triangle, we can find that the measurement of the angle ϴ is 48.8°, then the answer is option A. True.

Solution:

Using the Law of cosines:

a^2=b^2+c^2 - 2bc cos ϴ

with a=5.3, b=7, and c=4. Replacing the given values:

5.3^2=7^2+4^2 - 2(7)(4) cos ϴ

Squaring and multiplying:

28.09=49+16 - 56 cos ϴ

Adding on the right side of the equation:

28.09=65 - 56 cos ϴ

Solving for cos ϴ: Subtracting 65 both sides of the equation:

28.09-65=65 - 56 cos ϴ -65

Subtracting:

-36.91 = - 56 cos ϴ

Dividing both sides of the equation by -56:

(-36.91)/(-56)= (- 56 cos ϴ)/(-56)

0.659107143=cos ϴ

cos ϴ = 0.659107143

Solving for ϴ:

ϴ = cos^(-1) 0.659107143

ϴ = 48.76818605°

Rounding to one decimal place:

ϴ = 48.8°