Determine the number of solution for each possible triangle
B= 61 degrees a=12 b=8
The answer on the back of my book states zero.
Although I would think it has 2 because
12> b sin a when a is 29 degrees
Can anyone help me as I am slightly confused.
Determine the number of solution for each possible triangle
B= 61 degrees a=12 b=8
The answer on the back of my book states zero.
Although I would think it has 2 because
12> b sin a when a is 29 degrees
Can anyone help me as I am slightly confused.
The triangle must obey the Sine Law, however..
$\displaystyle \displaystyle\frac{sin61^o}{8}\ \ne\ \frac{sin29^o}{12}$
$\displaystyle \displaystyle\frac{sinA}{a}=\frac{sinB}{b}\Rightar row\ sinA=\frac{12sin61^o}{8}=1.312$
which is not possible, since
$\displaystyle -1\ \le\ sinA\ \le\ 1$
Wikipedia offers and explanation and drawing which is helpful.
Law of sines - Wikipedia, the free encyclopedia
Hello, homeylova223!
Determine the number of solution for this triangle:
. . $\displaystyle B= 61^o,\;a=12,\; b=8$
The answer on the back of my book states: zero..
If you had made a sketch, the answer would have been obvious.
Code:C * /:\ / : \ a=12 / : \ b=8 / : \ / : \ / : /61o : B * - - - + - - - * A D
Draw altitude $\displaystyle \,CD$ to side $\displaystyle \,AB.$
In right triangle $\displaystyle CDB\!:\;\sin61^o \:=\:\dfrac{CD}{12} \quad\Rightarrow\quad CD \:=\:12\sin61^o \;\approx\;10.5$
Side $\displaystyle \,b$ is only 8 units long.
There is no triangle.