Question

HOW MANY TRIANGLES CAN BE CONSTRUCTED WITH THE FOLLOWING MEASURES?

AB = 7.6 cm, AC = 5.4 cm, and m/_ABC = 50°.

Answer 1

No triangle can be constructed with given measures.

Explanation:

Refer the following figure.

AB = c = 7.6 cm

AC = b = 5.4 cm

∠ABC = B = 50°

Sine rule is given by
`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`

Substituting

`(5.4)/(sin50)=(7.6)/(sinC)\\\\sinC=1.078`

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

Hence no triangle can be constructed with given measures.