How do you solve the triangle given m∠A = 70°, c = 26, a = 25?

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Answer 1 · 2017-11-13T11:18:36

See below.

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From the information given, we can solve this using the Sine Rule:

The sine rule states that:

$sinA/a=sinB/b=sinC/c$

Finding angle C. Since we know angle A and side a, we will use:

$sinA/a=sinC/c$

$sin(70^o)/25=sinC/26=>sinC=(26sin(70^o))/25=0.9778$

$C=sin^-1(sinC)=sin^-1(0.9778)=color(blue)(77.76^o)$

Angle $B = 180^o-(70^o +77.76^o)=color(blue)(32.24^o)$

Side b:

$sin(70^o)/25=sin(32.24^o)/b=>b=(25sin(32.24^o))/sin(70^o)=color(blue)(14.19)$

So the solution is:

$A=70^o$

$B=32.24^o$

$C=77.76^o$

$a=25$

$b=14.19$

$c=26$