How many triangles are there that satisfy the conditions a=13, b=6, a= 6°

1 triangle is possible

Step-by-step explanation:

If there are two sides and a non included angle is given then there could be 0,1 or 2 triangles depend on the measure of the given angle and the lengths of the given sides.

We will discuss some conditions which will clarify that how many triangles are there in the given condition.

CASE 1: If A is obtuse and a>b then there is 1 triangle.

CASE 2: If A is obtuse and a<b then there is 0 triangle.

CASE 3:  If A is acute and a>b then there is 1 triangle.

CASE 4:  If A is acute  and h<a<b then there are 2  triangles possible.

CASE 5: If A is acute  and a=h then there is 1 right angle triangle.

CASE 6: If A is acute and a<h then there are 0 triangles possible.

Therefore according to the given condition A= 6° which is acute and a>b, So this condition matches the CASE 3:

According to this there is 1 triangle possible

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.