How many triangles can be constructed with the following measures?

ab = 7.6 cm, ac = 5.4 cm, and m/_abc = 50°.

AB=7.6 IS THE ANSWER OF THIS QUESTION

No triangle can be constructed with given measures.

Step-by-step explanation:

Refer the following figure.

     AB = c = 7.6 cm

     AC = b = 5.4 cm

     ∠ABC = B = 50°

Sine rule is given by

Substituting

Value of sinC is more than 1, which is not possible.

Hence no triangle can be constructed with given measures.

See answer below

Step-by-step explanation:

In inductive reasoning we arrive to a general conclusion based on particular observations.

For example:

"My friends Peter and Mary study at XYZ University. Peter and Mary are brilliant.

Yesterday I met Joe in a party. Joe also studies at XYZ University and he happens to be brilliant, too.

I conclude that all the students of XYZ University are brilliant"

Notice that this kind of reasoning might lead to a false conclusion.

In deductive reasoning, we arrive to a particular conclusion based on general observations. So, deductive reasoning is the opposite of inductive reasoning.

An example of deductive reasoning could be the following:

"To be accepted in the XYZ University you must pass a test with a score greater than 70%.

My friend Peter studies at XYZ University, so he passed the test with a score greater than 70%"

In deductive reasoning you may arrive to a false conclusion if your general assumption is false.