Answer: 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°