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Classify this triangle
by its sides and angles.
5.5 in
5.5in
1.5 in

User Wintersolutions
by
2.5k points

1 Answer

20 votes
20 votes

Answer:

Based on this sides and angles this triangle is an Acute isosceles triangle.

Explanation:

Calculating the triangle-

1.The triangle perimeter is the sum of the lengths of its three sides-

p = a+b+c = 5.5+5.5+1.5 = 12.5

2. The semi perimeter of the triangle-

The semi perimeter of the triangle is half its perimeter. By the triangle inequality, the longest side length of a triangle is less than the semi perimeter.

s= p/2=12.5/2=6.25

3. Heron's formula-

T=\sqrt(6.25-5.5)(6.25-5.5)(6.25-1.5))

=4.09

4.To calculate the heights of the triangle from its area=

(2*4.09)/5.5=1.49

(2*4.09)/5.5=1.49

(2*4.09)/1.5= 5.45

5. Finding the inner angles through the laws of Cosines

=82°9 ′45

=82°9 ′45"

15°40 ′30"

6.Inradius

=0.65

7. Circumradius

=2.78

8. Calculation of medians

=2.947

=2.947

=5.449

The two acute angles, opposites of two equal sides are also equal, making this an Acute isosceles triangle.

User Betagreg
by
2.7k points