Find the length of the third side. If necessary, round to the nearest tenth.
a is unknown
18
16
c2-b2=a2
Since c^2 - b^2 = a^2, we can substitute in the values given:
a^2 = c^2 - b^2
a^2 = 18^2 - 16^2
a^2 = 324 - 256
a^2 = 68
To find the length of the third side, we take the square root of both sides:
a = √68
a ≈ 8.2
Therefore, the length of the third side is approximately 8.2.
To find the length of the third side, 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, we have:
c^2 - b^2 = a^2
To find the length of the third side, we need to substitute the given values into the equation and solve for 'a'.
Let's do the calculation with the given values:
c^2 - b^2 = a^2
18^2 - 16^2 = a^2
324 - 256 = a^2
68 = a^2
To solve for 'a', we need to take the square root of both sides.
√68 = √(a^2)
8.246 = a
Rounding to the nearest tenth, the length of the third side is approximately 8.2.
To find the length of the third side (a) of a triangle when you have the lengths of the other two sides (b and c), you can use the Pythagorean theorem, which states that in a right-angled 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 other two sides.
In the equation you provided, c^2 - b^2 = a^2, we can use c as the hypotenuse and b as one of the other sides.
To find a, which is the length of the third side, we can rearrange the equation as follows:
a^2 = c^2 - b^2
Next, substitute the given values:
a^2 = 18^2 - 16^2
Now, calculate the equation:
a^2 = 324 - 256
a^2 = 68
To find the value of a, take the square root of both sides:
a = √68
Finally, simplify the square root:
a ≈ 8.246 (rounded to the nearest tenth)
Therefore, the length of the third side is approximately 8.246 units when rounded to the nearest tenth.