How do you solve the triangle given a=20, c=24, B=47?

Question

How do you solve the triangle given a=20, c=24, B=47?

1 Answer

Impact of this question

2473 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-16T09:24:34

Triangle is $a=20$ , $b=17.924$ , $c=24$ , $A=54.7^o$ , $B=47^o$ and $C=78.3^o$ .

Explanation:

Solving a triangle means identifying length of all the three sides as well as measures of all three angles. This is generally done using Law of sines, which is $a/sinA=b/sinB=c/sinC$ and Law of cosines, according to which $b^2=a^2+c^2-2ac cosB$ , $c^2=a^2+b^2-2abcosC$ and $a^2=b^2+c^2-2bc cosA$

Here, we are given $a=20$ , $c=24$ and $B=47^o$ .

We can use $b^2=20^2+24^2-2xx20xx24xxcos47^o$

= $400+576-960xx0.682=976-654.72=321.28$

Hence $b=sqrt321.28=17.924$

Now using ^^Law of sines**

$20/sinA=24/sinC=17.924/(sin47^o)=17.924/0.7314=24.5064$

Hence $sinA=20/24.5064=0.8161$ and $A=54.7^o$

and $sinC=24/24.5064=0.9793$ and $C=78.3^o$

Hence, triangle is $a=20$ , $b=17.924$ , $c=24$ , $A=54.7^o$ , $B=47^o$ and $C=78.3^o$ .

Science

Math

Humanities

... and beyond

How do you solve the triangle given a=20, c=24, B=47?

1 Answer

Explanation:

Related questions

Impact of this question