triangle ABC is shown in the diagram. The links of the sides are in terms of the variable n, where n >4. complete the inquali

Question

Dafna11 [192]

3 years ago

7

triangle ABC is shown in the diagram. The links of the sides are in terms of the variable n, where n >4. complete the inquali

ty

Mathematics

2 answers:

drek231 [11] · Answer 1 · 2022-06-25T12:00:06+03:00

drek231 [11]3 years ago

6 0

Answer:

M- B M-A M-C

Step-by-step explanation:

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Blababa [14] · Answer 2 · 2022-06-25T09:49:49+03:00

9514 1404 393

Answer:

m∠B < m∠A < m∠C

Step-by-step explanation:

We can work with the triangle inequality to find that the side measures form a triangle when n > 5/4. For the given value of n ≥ 4, we don't need to be concerned with whether a triangle is formed or not.

For n = 4, the side lengths are ...

a = 2(4) = 8

b = (4) +3 = 7

c = 3(4) -2 = 10

The longest side is opposite the largest angle, so the ordering of angles is ...

m∠B < m∠A < m∠C

_____

The triangle inequality requires all of these inequalities be true:

a+b > c ⇒ 3n+3 > 3n-2 . . . always true
b+c > a ⇒ 4n+1 > 2n ⇒ n > -1/2
c+a > b ⇒ 5n-2 > n+3 ⇒ n > 5/4

That will be the case for n > 5/4. The attached graph shows the sides and angles keep the same order for n > 3.