How to find the length of the side of a right triangle - Math

Using Pythagorean Theorem, we can solve for the length of leg x:

_x_2 + 22 = (√8)2 = 8

Now we solve for x:

_x_2 + 4 = 8

_x_2 = 8 – 4

_x_2 = 4

x = 2

We can use the Pythagorean Theorem to solve for x.

92 + _x_2 = 152

81 + _x_2 = 225

_x_2 = 144

x = 12

Using Pythagorean Theorem, we can solve for the length of leg x:

_x_2 + 62 = 102

Now we solve for x:

_x_2 + 36 = 100

_x_2 = 100 – 36

_x_2 = 64

x = 8

Also note that this is proportionally a 3/4/5 right triangle, which is very common. Always look out for a side-to-hypoteneuse ratio of 3/5 or 4/5, or a side-to-side ratio of 3/4, in any right triangle, so that you may solve such triangles rapidly.

The Pythagorean Theorem gives us _a_2 + _b_2 = _c_2 for a right triangle, where c is the hypotenuse and a and b are the smaller sides. Here a is equal to 5 and c is equal to 14, so _b_2 = 142 – 52 = 171. Therefore b is equal to the square root of 171 or approximately 13.07.

We use the Pythagorean Theorem and we calculate that 25 + 49 is not equal to 100.
All of the other answer choices observe the theorem _a_2 + _b_2 = _c_2

By virtue of the Pythagorean Theorem, in a right triangle the sum of the squares of the smaller two sides equals the square of the largest side. Only 9, 12, and 15 fit this rule.

Using the Pythagorean Theorem, the height of the right triangle is found to be = √(〖15〗2 –〖12〗2) = 9, so x=9 – 5=4

use the pythagorean theorem:

a2 + b2 = c2 ; a and b are sides, c is the hypotenuse

a2 + 1296 = 1521

a2 = 225

a = 15

Using the pythagorean theorem, 82=72+x2. Solving for x yields the square root of 15, which is 3.9

Area= $\frac{1}{2}$times basetimes height

42=\frac{1}{2}$times basetimes 12

42=6times base

base=7

AB is the leg adjacent to Angle A and BC is the leg opposite Angle A.

Since we have a triangle, the opposites sides of those angles will be in the ratio .

Here, we know the side opposite the sixty degree angle. Thus, we can set that value equal to .

which also means

The length of segment $\overline{BD}$ is $\frac{4sqrt{3}$}{3}

Note that triangles ACD and BCD are both special, 30-60-90 right triangles. Looking specifically at triangle ACD, because we know that segment $\overline{AD}$ has a length of 4, we can determine that the length of segment $\overline{CD}$ is 2 using what we know about special right triangles. Then, looking at triangle BCD now, we can use the same rules to determine that segment $\overline{BD}$ has a length of $\frac{4}{sqrt{3}$}

which simplifies to $\frac{4sqrt{3}$}{3}.

Use the Pythagorean Theorem. The sum of both legs squared equals the hypotenuse squared.

Use the Pythagorean Theorem. Let a = 8 and c = 10 (because it is the hypotenuse)

$a^2$$+x^2$$=c^2$

$8^2$$+x^2$$=10^2$

$64+x^2$=100

$x^2$=100-64=36

x=6

We will use the Pythagorean Theorem to solve for the missing side length.

Since the perimeter of the ring is feet and the ring is a square, solve for the length of a single side of the ring by dividing by .

The distance between the two boxers in opposing corners is a straight line from any one corner to the other. That straight line forms the hypotenuse of a right triangle whose other two sides are each feet long (since they are each the sides of the square).

Solving for the length of the hypotenuse of this right triangle with the pythagorean theorem provides the distance between the two boxers when they are in opposite corners.

Use the Pythagorean theorem: .

We know the length of one side and the hypotenuse.

Now we can solve for the missing side.

Use the Pythagorean Theorem to solve for the missing side of the right triangle.

In this triangle, .

Now we can solve for .

This image depicts a 30-60-90 right triangle. The length of the side opposite the smallest angle is half the length of the hypotenuse.