In triangle ABC, if $a = 8.75$ $a = 8.75$ centimeters, $c = 4.26$ $c = 4.26$ centimeters, and $m ∠ B$ $m/_B$ is $87°$ what is the length of $b$ to two decimal places?

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Answer 1 · 2018-08-13T07:07:42

$:.b~~9.53 " cm"$

We know that ,

$color(red)("cosine Rule : " cosB=(c^2+a^2-b^2)/(2ca))$

$:.2cacosB=c^2+a^2-b^2$

$:.b^2=c^2+a^2-2cacosB...to(1)$

We have ,

$a=8.75" cm" ,$ , $c=4.26 " cm" and B=87^circ$

Using $(1)$ we get

$b^2=(4.26)^2+(8.75)^2-2(4.26)(8.75)cos87^circ$

$:.b^2=18.1476+76.5625-74.55(0.0523)$

$:.b^2~~90.81135$

$:.b~~9.529$ cm

In triangle ABC, if a = 8.75a=8.75a = 8.75 centimeters, c = 4.26c=4.26c = 4.26 centimeters, and m/_Bm∠Bm/_B is 87°87° what is the length of bb to two decimal places?