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The side of a triangle are in the ratio 5:6:3. Find the smallest and biggest...

The side of a triangle are in the ratio 5:6:3. Find the smallest and biggest angle?

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Answers (10)

Maranatha
1 week ago
The question may look weird but the only way to solve it is using the Cosine and sine rules.

First of all Note that if the size of a side of a triangle corresponds with the angle opposing that side.

In other words, the angle facing the triangle side that is 6. Is the biggest, while the one facing side 3 is the smallest.


First of all I'll attach the value of the sides of the triangle to an actual triangle BELOW.
  • Maranatha: Now, we can use the cosine rule to solve for A. Since it's obviously the smallest.
    NB. A is opposite a=3. Thus, it's the smallest angle.
    Like 1    Dislike 0   1 week ago
  • Maranatha: Having found the smallest angle. At least we now have 1 angle and three side. Now we can use sine rule to find the biggest angle. Which is C.
    Like 1    Dislike 0   1 week ago
Dolly P
1 week ago
Sum of angles in a triangle=180 degrees

Ratio=5:6:3
Summation= 5+6+3=14

First angle = 5/14x180=64.3 degree

Second angle= 6/14x180=77.1 degree

Third angle= 3/14x180=38.6 degree

Therefore,the biggest angle is 77.1 degree

while the smallest is 38.6 degree
Michaelsuccess
1 week ago
Hello
Michaelsuccess
1 week ago
5+6+3=14
Hence;
5/14,
6/14(3/7),
3/14.

The biggest size is 6/14, why the smallest size is 3/14
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