Triangle JKL, where KL = 8 cm, JK = 6 cm and <JKL = 90°
so it is twice a 3,4,5 right triangle
sides are 2*3 , 2*4 and hypotenuse is therefore 10
make absolutely certain that
10^2 = 6^2 + 8^2
then what else is there ?
cos JLK = 0.8
third angle is 90 - that
etc.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, given that <JKL = 90° and KL = 8 cm, JK = 6 cm, we need to find the length of the remaining side JL.
Using the Pythagorean theorem, we can write the equation as:
JL^2 = JK^2 + KL^2
Substituting the given values:
JL^2 = 6^2 + 8^2
JL^2 = 36 + 64
JL^2 = 100
Taking the square root of both sides, we have:
JL = √100
JL = 10 cm
Therefore, the length of the side JL is 10 cm.
To find the remaining side length of Triangle JKL, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, KL is the hypotenuse and JK is one of the other sides. Let's label the remaining side as JL.
The Pythagorean theorem states:
KL^2 = JK^2 + JL^2
Substituting the given values:
8^2 = 6^2 + JL^2
Simplifying the equation:
64 = 36 + JL^2
Now, we can isolate JL by subtracting 36 from both sides:
28 = JL^2
To solve for JL, we can take the square root of both sides:
√28 = √JL^2
Simplifying further:
√28 = JL
By evaluating the square root of 28, we find that JL is approximately 5.29 cm.