Solve Triangle: a=6, b=8, c=10
Complete solution for the triangle with given measurements. Find all missing sides, angles, area, and perimeter.
Area: 24 sq units
Perimeter: 24 units
Step-by-Step Solution
Step 1
Given Information
Sides: a = 6, b = 8, c = 10
Angles: A = ?°, B = ?°, C = ?°
Step 2
Method: SSS (Side-Side-Side)
All three sides are known
Use Law of Cosines to find angles
Step 3
Find Angles (Law of Cosines)
cos(A) = (b² + c² - a²) / (2bc) = 0.8
A = 36.87°
cos(B) = (a² + c² - b²) / (2ac) = 0.6
B = 53.13°
C = 180° - A - B = 90°
Step 4
Calculate Area (Heron's Formula)
s = (a + b + c) / 2 = 12
Area = √[s(s-a)(s-b)(s-c)]
Area = √[12 × 6 × 4 × 2]
Area = 24
Step 5
Perimeter
P = a + b + c = 24
Step 6
Triangle Classification
Scalene (no sides equal)
Right triangle (one 90° angle)
Step 7
Final Answer
A = 36.87°, B = 53.13°, C = 90°, Area = 24
Triangle Solution Methods
SSS (3 sides): Use Law of Cosines for angles, Heron's for area
SAS (2 sides, included angle): Use Law of Cosines
ASA/AAS (2 angles, 1 side): Use Law of Sines