Find the missing length. Round to the nearest tenth, if necessary.
A right triangle has legs measuring 8 units and x units and a hypotenuse measuring 21 units.
General Idea:
By using the Pythagorean theorem which states that in a right triangle the sum of square of two legs is equal to the square of hypotenuse. We can find the length of the third side.
Given:
We can see shortest side a is 4 inches, hypotenuse is c is 8 inches and middle side is 4√3. This is quality of a special triangle. The smallest side (a) is opposite the smallest angle (30°), the middle side (b) is opposite the angle (60°) and the longest side (c) is opposite the largest angle (90°).
The triangle 30°-60° - 90° triangle will be of the ratio 1:√3:2.
Conclusion:
The length of the other leg is 4√3 in
The measures of the acute angles are : 30° and 60°
Oops wrong problem
x^2 + 8^2 = 21^2
x^2 + 64 = 441
x^2 = 377
x = sqrt(377) = appr 19.42
To find the missing length, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
In this case, we are given the lengths of the legs (8 units and x units) and the length of the hypotenuse (21 units). Let's substitute these values into the Pythagorean theorem:
8^2 + x^2 = 21^2
Simplifying the equation, we get:
64 + x^2 = 441
Next, let's isolate x by subtracting 64 from both sides:
x^2 = 441 - 64
x^2 = 377
To find x, we need to take the square root of both sides:
x = √377
Using a calculator, we find that √377 is approximately 19.4 units.
Therefore, the missing length, rounded to the nearest tenth, is 19.4 units.