find k if (9,60,k) is a pythagoras triplet
Answers
Step-by-step explanation:
Pythagoras Theorem
The Pythagoras theorem states that, "the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides".
The basic formula to calculate hypotenuse is a² + b² = c², where c represents the length of the hypotenuse and a and b are the lengths of the triangle's other two sides.
If the length of both a and b are known, then c can be calculated as
In this triangle, c2=a2 + b2
Although Pythagoras theorem is applicable in case of a right-angled triangle only, yet it has a lot of direct and indirect applications.
Classification of triangles on Pythagoras theorem:
If a2 + b2 < c2, then the triangle would be an obtuse-angled triangle.
If a2 + b2 > c2, then the triangle would be an acute-angled triangle.
Let us see its application in solving questions.
Example: Find the number of acute triangles that can be formed with two of its sides equal to 8, 15.
Solution: For an acute triangle, we have condition a2 + b2 > c2
Other condition that we'll use is: The sum of 2 sides in a triangle is greater than the third side.
Let the third side be x.
Applying the first condition, we get
82+x2 > 152; 82+152 >x2; x2+15>82
x2>225-64 ⇒ x2 >161 => Since x is an integer, x=13,14,15,16,17,....
82+152 >x2 ⇒ 289>x2 => x=0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16.
x2+15>82⇒x>0
Applying the second condition, we get
8+15>x; 8+x>15; 15+x>8
⇒x<23; x>7; x> -7
&rArr Combining the two conditions, we get x=13, 14, 15, 16.
Hence we get 4 cases. Answer= 4
Answer:
your answer is 4 .
Step-by-step explanation: