Question

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​

Answer 1

Answer:

See below

Step-by-step explanation:

to understand this

you need to know about:

• law of sine
• law of cosine
• PEMDAS

let'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 angles
• and 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

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

$\bold{= 100.64}$