How do you determine whether $△ A B C$ $triangle ABC$ has no, one, or two solutions given $A = 30^{\circ}, a = 3, b = 6$ $A=30^circ, a=3, b=6$ ?

Question

How do you determine whether $△ A B C$ $triangle ABC$ has no, one, or two solutions given $A = 30^{\circ}, a = 3, b = 6$ $A=30^circ, a=3, b=6$ ?

1 Answer

Impact of this question

1930 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-19T09:29:32

One triangle.

Explanation:

In this particular case we're given $A = 30^{\circ}$ $A=30^circ$ and $a = 3$ $a=3$ , which is the side opposite $A$ $A$ . Since $b = 6 = 2 a$ $b=6=2a$ we actually know that we're dealing with a $30^{\circ}$ $30^circ$ - $60^{\circ}$ $60^circ$ - $90^{\circ}$ $90^circ$ triangle because of the ratio of sides: $x - x \sqrt{3} - 2 x$ $x-xsqrt(3)-2x$ . In this case there is exactly one triangle and we don't really need to use the Law of Sines.

If you want to use the law of sines, though, calculate $6 \cdot sin (30^{\circ}) = 6 (\frac{1}{2}) = 3$ $6*sin(30^circ) = 6(1/2)=3$ which is exactly the length of $a$ $a$ , the side opposite the given angle, which means we have one right triangle solution.

Science

Math

Humanities

... and beyond

How do you determine whether $△ A B C$ $triangle ABC$ has no, one, or two solutions given $A = 30^{\circ}, a = 3, b = 6$ $A=30^circ, a=3, b=6$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you determine whether △ABCtriangle ABC has no, one, or two solutions given A=30∘,a=3,b=6A=30^circ, a=3, b=6?

1 Answer

Explanation:

Related questions

Impact of this question

How do you determine whether $△ A B C$ $triangle ABC$ has no, one, or two solutions given $A = 30^{\circ}, a = 3, b = 6$ $A=30^circ, a=3, b=6$ ?