Answer:
13
Step-by-step explanation:
From the question, we are given a triangle HNK with an angle of 90°
The length of hypotenuse H K is n,
the length of HN is 12
the length of N K is 6.
From the above values, obtained in the question, we can see that this is a right angled triangle.
We are asked to find the length of the hypotenuse.
We can use Pythagoras Theorem of solve for this.
c² = a² + b²
where c = HK = n
a = NK = 6
b = HN = 12
c² = 6² + 12²
c² = 36 + 144
c² = 180
c = √180
c = 13.416407865
Approximately to the nearest whole number = 13
Therefore the value of HK = n = 13
We can also use Law of Cosines as given in the question to solve for this.
a² = b² + c² - 2ac × Cos A
where c = HK = n
a = NK = 6
b = HN = 12
Hence
c² = a² + b² - 2ab × Cos C
c = √ (a² + b² - 2ab × Cos C)
Where C = 90
c = √ 6² + 12² - 2 × 6 × 12 × Cos 90
c = 13.42
Approximately to the nearest whole number ≈ 13
Therefore the value of HK = n = 13
