Answer:
6.55 cm
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, acute, scalene, obtuse, right and equilateral triangle.
Cosine rule is used to show the relationship between sides and angles of a triangle. If a, b, and c are sides of a triangle, while A, B, and C are angles opposite to the corresponding sides. Then:
c² = a² + b² - 2ab*cos(C)
Given that PR = 13 cm, PQ = 12 cm and angle QPR = 30°, hence:
QR² = PR² + PQ² - 2(PR)(PQ)cos(∠QPR)
QR² = 13² + 12² - 2(13)(12)cos(30) = 169 + 144 - 270
QR² = 43
QR = 6.55 cm
 
        
             
        
        
        
Answer:
a - 12 seconds (1/5 minute)
b - 5
Step-by-step explanation:
 
        
                    
             
        
        
        
Answer:
x = 24
Step-by-step explanation:
(2x - 4) + (3x + 5) + (2x + 11) = 180°
Combine like terms:
7x + 12 = 180
Subtract 12 on both sides:
7x = 168
Divide 7 on both sides:
x = 24
 
        
                    
             
        
        
        
Answer:
x = 14
Step-by-step explanation:
The polygon given has 6 sides
Sum of interior angles of a 6-sided polygon = 180(n - 2)
substitute n = 6 into 180(n - 2)
Sum of the polygon = 180(6 - 2) = 720°
Thus:
10x + 8x - 16 + 12x - 8 + 7x + 2 + 9x + 4 + 6x + 10 = 720
Add like terms 
52x - 8 = 720
52x = 720 + 8
52x = 728
x = 728/52
x = 14