Question #205675

Solve the triangle.


A = 52°, b = 14, c = 6


1
Expert's answer
2021-06-14T19:02:31-0400

Answer:


B=103.8° , a=11.3 and C=24.2°


Given:

A = 52°, b = 14, c = 6


using sine law:

asinA=bsinB=csinC{a\over sinA}={b\over sinB}={c\over sinC}


asin52o=14sinB=6sinC{a\over sin52^o}={14\over sinB}={6\over sinC} ..........................1


using cosine law:


a2=b2+c22bcCosAa^2=b^2+c^2-2bcCosA


a2=196+362(14)(6)Cos52oa^2=196+36-2(14)(6)Cos52^o .............2

from 2 we get,

a=11.3 ........................3


putting 3 in 1

And solving

11.3sin52o=14sinB{11.3\over sin52^o}={14\over sinB}

And

11.3sin52o=6sinC{11.3\over sin52^o}={6\over sinC}

As we see first possible solution

we get

B=103.80

C=24.20




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