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victus00 [196]
3 years ago
9

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

Mathematics
1 answer:
creativ13 [48]3 years ago
4 0
<h3>Answer:</h3><h3>See below</h3>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>
  • law of sine
  • law of cosine
  • PEMDAS
<h3>let's solve:</h3>

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}

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