7. in $ \triangle a b c, m \angle a = 40 ^ { \circ }, m \angle b = 75 ^ { \circ } $, and $ m \angle c = 65 ^ { \circ } $. which list has the sides of $ \triangle a b c $ in order from longest to shortest?
(1) $ a c b c a b $
(2) $ b c a b a c $
(3) $ a b a c b c $
(4) $ a c a b b c $

Question

7. in $ \triangle a b c, m \angle a = 40 ^ { \circ }, m \angle b = 75 ^ { \circ } $, and $ m \angle c = 65 ^ { \circ } $. which list has the sides of $ \triangle a b c $ in order from longest to shortest?
(1) $ a c > b c > a b $
(2) $ b c > a b > a c $
(3) $ a b > a c > b c $
(4) $ a c > a b > b c $

Accepted Answer

# Explanation:
## Step1: Recall the triangle side - angle relationship
In a triangle, the larger the angle, the longer the side opposite it.
## Step2: Compare the angles
We have $m\angle B=75^{\circ}$, $m\angle C = 65^{\circ}$, $m\angle A=40^{\circ}$. So $\angle B>\angle C>\angle A$.
## Step3: Determine the sides opposite the angles
Side $AC$ is opposite $\angle B$, side $AB$ is opposite $\angle C$, and side $BC$ is opposite $\angle A$.

# Answer:
$AC>AB > BC$, so the answer is (4).

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the triangle side - angle relationship

Step2: Compare the angles

Step3: Determine the sides opposite the angles

Answer: