Question

In △ABC, A-68°,a= 14 and c=17. Which of these statements best describes the triangle?

A. △ABC is acute
B. △ABC is obtuse
C. △ABC can be either acute or obtuse.
D. △ABC is a right triangle
E. △ABC cannot be constructed

Answer 1

According to the information provided, triangle ABC cannot be constructed (option E).

Let's use the Law of Sines to find the measure of angle B in triangle ABC.

The Law of Sines states:
`(a)/(sinA) =(b)/(sinB) =(c)/(sinC)`

Given:

A=68

a=14,

c=17

We have a=14 and c=17. We need to find angle

B, and then we can find angle

C using the fact that the sum of angles in a triangle is 180

Let's find angle B using the Law of Sines:

`(a)/(sinA) = (c)/(sin C)`

`(14)/(sin 68) = (17)/(sin C)`

First, find sin68∘ :

sin68 ≈0.927

Now, solve for sinC:

​
`(14)/(0.927) = (17)/(sin C)`

sinC≈ 17×0.927/ 14

sinC≈1.123

However, sinC cannot be greater than 1, which means the given information doesn't create a valid triangle. Therefore, according to the information provided, triangle ABC cannot be constructed (option E).