How do you solve a triangle given a=10 b=8 B=130 degrees?

Question

How do you solve a triangle given a=10 b=8 B=130 degrees?

1 Answer

Impact of this question

3272 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-09T18:07:16

The Law of Sines

Explanation:

The Law of Sines states

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a/(sinA)=b/(sinB)=c/(sinC)$

We are given $a$ $a$ $b$ $b$ and $B$ $B$ so we can set them equal to each other and solve for Sin of A

$\frac{10}{sin A}$ $10/(sinA)$ = $\frac{8}{sin 130}$ $8/(sin130)$

manipulating that you get $\frac{10 sin 130}{8}$ $(10sin130)/(8)$ = $0.95755$ $0.95755$

Taking the inverse ${sin}^{- 1} (0.95755)$ $sin^-1(0.95755)$ = $73.13$ $73.13$

This is the angle A. If you have 2 angles of a triangle you really have 3 angles. Just take the sum of the two known angles and subtract them from 180.

$(130 + 73.13) - 180 = 23.13$ $(130+73.13)-180=23.13$

Now that you have all three angles you can use the cosine equation

$c^{2} = a^{2} + b^{2} - 2 a b cos C$ $c^2=a^2+b^2-2abcosC$

$c^{2} = 8^{2} + 10^{2} - (10 \cdot 8) cos 23.13$ $c^2=8^2+10^2- (10*8) cos23.13$

$c^{2} = 16.86$ $c^2=16.86$

$\sqrt{c^{2}} = \sqrt{16.86}$ $sqrt(c^2)=sqrt(16.86)$

$c = 4.1$ $c=4.1$

I hope that helps.

Science

Math

Humanities

... and beyond

How do you solve a triangle given a=10 b=8 B=130 degrees?

1 Answer

Explanation:

Related questions

Impact of this question