Mathematics: Find the area of the triangle with the given measurements. round the solution to the nearest hundredth if necessary. b = 104°, a = 11 cm, c = 18 cm

Find the area of the triangle with the given

Ответ:

dumbdumbkylee

17.01.2022

$\bf \textit{Law of Cosines}\\ \quad \\
c^2 = {{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)\implies 
c = \sqrt{{{ a}}^2+{{ b}}^2-(2{{ a}}{{ b}})cos(C)}\\\\
-----------------------------\\\\
b = \sqrt{{{ a}}^2+{{ c}}^2-(2{{ a}}{{ c}})cos(B)}
\\\\\\
b=\sqrt{{{ 11}}^2+{{ 18}}^2-2(11\cdot 18)cos(104^o)}
\\\\\\
b\approx 23.25512998582180400481\implies b\approx 23.26$

so, "b" rounded up is 23.26, now, we know a = 11 and c = 18

well, to get the area then, let us use Heron's formula

$\bf \textit{Heron's Area formula}\\\\
A=\sqrt{s(s-a)(s-b)(s-c)}\qquad 
\begin{cases}
a=11\\
c=18\\
b\approx 23.26\\\\
s=\cfrac{a+b+c}{2}
\end{cases}$

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Ответ:

alyssacruz999

20.01.2023

Mathematics

u need to subtract the pool from the whole area to get the answer

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

b = 104°, a = 11 cm, c = 18 cm

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