Question

If in ️ABC, angle A = 30 , angle C =60 find AB​

Answer 1

Answer:

Step-by-step explanation:

$<A=30\\<C=60\\=>\;\;<B=90\;\;\;|by\;angle\;sum\;property|$

Now, since It's a right angles triangle, we can apply trigonometry  to find AB.

BUT, since no other side is given, we can only find AB in form of variables like$x,y,\alpha,\beta,\gamma,a,n,c,d,etc.$

SO, I know your question is incomplete, but I'll still give you the answer in the form of sides, in which you can plug in the values of sides that you would be knowing to get the value of AB

SO,

AB can be found using  following ways-

$sin60=\frac{AB}{AC}=\frac{\sqrt3}{2}\\\\sin30=\frac{BC}{AC}=\frac{1}{2}\\\\ } \\\\cos60= \frac{BC}{AC}=\frac{1}{2}\\\\cos30=\frac{AB}{AC}=\frac{\sqrt3}{2}\\\\tan30=\frac{BC}{AB}=\frac{1}{\sqrt3}\\\\tan60=\frac{AB}{BC}=\sqrt3 \\\\cot30=\frac{AB}{BC}=\sqrt3 \\\\cot60=\frac{BC}{AB}=\frac{1}{\sqrt3}$

SO, according to your comfort, you can use the one with which you can find the answer easily

e.g. suppose that you know that BC= 10 cm

then you can apply

$tan\theta\\cot\theta$

anyone which you like,

I am using

$tan60=\frac{AB}{BC}=\sqrt3\\=>\frac{AB}{10}=\sqrt3\\=>AB=10\sqrt3$

Just an example.

$Learning\;\;together\;:)$