Question

The sides of a triangle are 3.4 cm, 4.7 cm, and 6.3 cm long. The angle opposite the side that is 4.7 cm long measures 47°. Which angle could be opposite the side that is 3.4 cm long?

Answer 1

just use the cosine formula
you have a triangle ABC like this-
cosine formula is->
\(\huge cosA=\Huge \frac{b^2+c^2-a^2}{2bc}\)

here we take \(a=3.4, ~~~~b=4.7~~~and~~~c=6.3\)
just put them in equation you get this-

\(\Large cosA=\huge\frac{4.7^2+6.3^2-3.4^2}{2(4.7)(6.3)}\)

simplifying we get->
\(cosA=0.848\)
so \(A=\cos^{-1} (0.84802)\)
so A=32 degrees