Mathematics: Calculate the unknown sides and angles of the triangle ABC given. Given the final answer correct to three significant figures. C= 25.7° , b= 3.5cm, a = 6cm

DStep-by-step explanation:Sum up, subtract and simplify...

Calculate the unknown sides and angles of the triangle

Ответ:

kylee76

20.04.2021

Mathematics

See below

Step-by-step explanation:

to understand thisyou need to know about:law of sinelaw of cosinePEMDASlet's solve:

there are 3 ways to solve SAS triangle

use The Law of Cosines to calculate the unknown side,then use The Law of Sines to find the smaller of the other two anglesand then use the three angles add to 180° to find the last angle.

first figure out $\angle C$

to do so we will use the formula of law of cosine of C angle

${c}^{2} = {a}^{2} + {b}^{2} - 2ab.\cos(C)$

substitute the given values of a,b and $\angle C$

$\sf{c}^{2} = {6 }^{2} + {3.5}^{2} - 2.6.(3.5). \cos( {25.7}^{ \circ} )$

simplify squares:

$c^{2}=36+12.25-42.\cos(25.7^{\circ})$

simplify addition:

$c^{2}=48.25-42.\cos(25.7^{\circ})$

square root both sides

$\sf \: \sqrt{ {c}^{2} } = \sqrt{ 48.25-42. \cos(25.7^{\circ})}$

simplify:

therefore

$\bold{c=3.23}$

use law of sine to figure out angle A

$\dfrac{6}{\sin( \angle \: A) } = \dfrac{3.23}{\sin(25.7)}$

therefore

$\bold{\angle A=53.66°}$ (use calculater to simplify it)

therefore

$\angle B\: is\: 180^{o}-25.70^{o}-53.66^{o}$

$\bold{= 100.64}$

Calculate the unknown sides and angles of the triangle ABC given.

Given the final answer correct to

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Calculate the unknown sides and angles of the triangle ABC given. Given the final answer correct to three significant figures.
C= 25.7° , b= 3.5cm, a = 6cm

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Calculate the unknown sides and angles of the triangle ABC given. Given the final answer correct to three significant figures. C= 25.7° , b= 3.5cm, a = 6cm​

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Calculate the unknown sides and angles of the triangle ABC given. Given the final answer correct to three significant figures.
C= 25.7° , b= 3.5cm, a = 6cm