Question

7. In a triangle ABC, A = 30°, a= 2 and c= 5 then C equals to
A) 60°
B) 90°
C) 75°

and please answer sincerely.
Requires steps tooo​

Answer 1

Answer:

In triangle ABC, AB = c = 3, AC = b = 4 and <BAC = 60 deg. What is BC = a?

We can apply the cosine formula

a^2 = b^2 + c^2 - 2bc cos C

= 4^2+3^2–2*4*3*cos 60

= 4^2+3^2–2*4*3*0.5

= 16+9–12

= 13

BC = a = 13^0.5 = 3.605551275 cm

Answer 2

We need to recall the following sine law of a triangle.

Low of sine: $\frac{sinA}{a} =\frac{sinB}{b}=\frac{sinC}{c}$

This problem is about the sine law.

Given:

In a Δ ABC, $\angle\ A=30\textdegree$ , $a=2$ and $c=5$

From the sine law of a triangle, we get

$\frac{sinA}{a}=\frac{sinC}{c}$

$\frac{sin30\textdegree}{2}=\frac{sinC}{5}$

$\frac{\frac{1}{2} }{2}=\frac{sinC}{5}$

$sinC=\frac{5}{4}$

$C=sin^{-1}(\frac{5}{4} )$