Question

The measure of in degrees, is approximately 34.38 side lengths are 4, 5.3 ,and 7

Answer 1

For 4^2+7^2-5.3^2 it equal 36.91 now for 2ab is that like this 2(4)(7) which equals 56 so is it supposed to look like this 36.91/56 which equals 0.66.

(theta)=cos^-1(0.66)

theta=0.849978 or 0.85 (I guess this is in radian form)

Converting it to degrees I think it is 0.85 = 48.70 degrees

48.70 does not equal 34.38 degrees so false right?

I think the answer is false. Is this correct did I make any mistakes? Please explain. Thank you!

Answer 2

Draw the triangle as shown in the figure below.
a=5.3, b=7, c=4.

The smallest angle is ∠C because it is opposite the shortest length of 4.
From the Law of Cosines,
c² = a² + b² - 2ab cosC
or
cos C = (a² + b² - c²)/(2ab)
= (5.3² + 7² - 4²)/(2*5.3*7)
= 0.823

∠C = arcos(0.823) = 34.58°
This answer agrees reasonably with 34.38°