Question

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.

B = 74°, a = 14 cm, c = 20 cm

Answer 1

c

Answer 2

have you covered the Law of Cosines yet?

Answer 3

yes

Answer 4

ok... so we would want to find the side "b" then so \(\bf \textit{Law of Cosines}\\ \quad \\
b^2 = {\color{blue}{ a}}^2+{\color{red}{ c}}^2-(2{\color{blue}{ a}}{\color{red}{ c}})cos(B)\implies
b = \sqrt{{\color{blue}{ a}}^2+{\color{red}{ c}}^2-(2{\color{blue}{ a}}{\color{red}{ c}})cos(B)}
\\ \quad \\
thus\implies b=\sqrt{14^2+20^2-(2\cdot 14\cdot 20)\cdot cos(74^o)}\)

Answer 5

b=21.0153

Answer 6

yeap.... so now we know the sides "a", "b" and "c"

so to get the area of a triangle, with only the sides length
we could just use Heron's Formula, that is \(\bf {\color{purple}{ s}}=\cfrac{a+b+c}{2}
\\ \quad \\
\textit{area of a triangle}=\sqrt{{\color{purple}{ s}}({\color{purple}{ s}}-a)({\color{purple}{ s}}-b)({\color{purple}{ s}}-c)}\)

Answer 7

Thanks, can you help me check something else?

Answer 8

I'd be dashing soon... so is better to post anew anyhow... so if I dunno... someone else may

Answer 9

ok