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

See below

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

`(6)/(\sin( \angle \: A) ) = (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}`