SOLUTION: The sides of a triangle are in the ratio of 4:5:6. What is the smallest angle? Please help me to answer this. Thanks.

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Question 1053236: The sides of a triangle are in the ratio of 4:5:6. What is the smallest angle? Please help me to answer this. Thanks.
Found 3 solutions by ewatrrr, ikleyn, Alan3354:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  

 Let x represent the constant of proportionality

4x + 5x + 6x = 180°

15x = 180°

x = 12°

Angles: 48°, 60°, 72°  (Sum 180° CHECKS!)

smallest 48°

Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
.
Theorem.

If a triangle has the sides proportional with 4:5:6, then the smallest angle measure is half of the biggest angle measure.

For the proof, see the lesson
    - Triangle with the sides ratio 4:5:6 has the smallest angle measure half of the biggest angle
in this site.

You have this free of charge online textbook on Geometry
    - GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lesson is the part of this textbook under the topic "Miscellaneous advanced Geometry problems".


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sides of a triangle are in the ratio of 4:5:6. What is the smallest angle?
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Use sides of 4, 5 & 6.
The smallest angle is opposite the shortest side.
Use the Cosine Law to find the angle opposite the side of length 4.