QuestionFind the missing side of a right triangle with sides 6.5 and 4. Round your answer to the nearest hundredth. Use $a^2 + b^2 = c^2$ .

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. The lengths of two sides are given6.5 and43. We are looking for the length of the missing side, which could either be the hypotenuse or one of the legs, depending on the given sides4. The Pythagorean theorem applies to right triangles and states that 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. We will use this theorem to find the missing side.

STEP 2

First, we need to determine whether the given sides are the hypotenuse or the legs of the triangle. The hypotenuse is always the longest side in a right triangle, so if one of the given sides is longer than the other, that side is the hypotenuse.

STEP 3

In this case, the longer side is6.5, so we will assume that this is the hypotenuse. The other side,, is one of the legs. We are looking for the length of the other leg.

STEP 4

We can use the Pythagorean theorem to find the length of the missing side. The theorem is written as follows $c^2 = a^2 + b^2$ where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

STEP 5

We can rearrange the Pythagorean theorem to solve for the missing side (let's call it a):
$a = \sqrt{c^2 - b^2}$

STEP 6

Now, plug in the given values for the hypotenuse (c) and the known leg (b) to calculate the length of the missing side (a).
$a = \sqrt{6.5^2 -4^2}$

STEP 7

Calculate the square of each side.
$a = \sqrt{42.25 -16}$

STEP 8

Subtract the square of the known leg from the square of the hypotenuse.
$a = \sqrt{26.25}$

STEP 9

Take the square root of the result to find the length of the missing side.
$a =5.12$ The length of the missing side of the triangle is approximately5.12, rounded to the nearest hundredth.

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QuestionFind the missing side of a right triangle with sides 6.5 and 4. Round your answer to the nearest hundredth. Use $a^2 + b^2 = c^2$ .

Studdy Solution

STEP 1

STEP 2

First, we need to determine whether the given sides are the hypotenuse or the legs of the triangle. The hypotenuse is always the longest side in a right triangle, so if one of the given sides is longer than the other, that side is the hypotenuse.

STEP 3

In this case, the longer side is6.5, so we will assume that this is the hypotenuse. The other side,, is one of the legs. We are looking for the length of the other leg.

STEP 4

We can use the Pythagorean theorem to find the length of the missing side. The theorem is written as follows $c^2 = a^2 + b^2$ where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

STEP 5

We can rearrange the Pythagorean theorem to solve for the missing side (let's call it a):
$a = \sqrt{c^2 - b^2}$

STEP 6

Now, plug in the given values for the hypotenuse (c) and the known leg (b) to calculate the length of the missing side (a).
$a = \sqrt{6.5^2 -4^2}$

STEP 7

Calculate the square of each side.
$a = \sqrt{42.25 -16}$

STEP 8

Subtract the square of the known leg from the square of the hypotenuse.
$a = \sqrt{26.25}$

STEP 9

Take the square root of the result to find the length of the missing side.
$a =5.12$ The length of the missing side of the triangle is approximately5.12, rounded to the nearest hundredth.

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QuestionFind the missing side of a right triangle with sides 6.5 and 4. Round your answer to the nearest hundredth. Use a2+b2=c2a^2 + b^2 = c^2a2+b2=c2.

Studdy Solution

STEP 1

STEP 2

First, we need to determine whether the given sides are the hypotenuse or the legs of the triangle. The hypotenuse is always the longest side in a right triangle, so if one of the given sides is longer than the other, that side is the hypotenuse.

STEP 3

In this case, the longer side is6.5, so we will assume that this is the hypotenuse. The other side,, is one of the legs. We are looking for the length of the other leg.

STEP 4

We can use the Pythagorean theorem to find the length of the missing side. The theorem is written as followsc2=a2+b2c^2 = a^2 + b^2c2=a2+b2where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

STEP 5

We can rearrange the Pythagorean theorem to solve for the missing side (let's call it a):a=c2−b2a = \sqrt{c^2 - b^2}a=c2−b2​

STEP 6

Now, plug in the given values for the hypotenuse (c) and the known leg (b) to calculate the length of the missing side (a).a=6.52−42a = \sqrt{6.5^2 -4^2}a=6.52−42​

STEP 7

Calculate the square of each side.a=42.25−16a = \sqrt{42.25 -16}a=42.25−16​

STEP 8

Subtract the square of the known leg from the square of the hypotenuse.a=26.25a = \sqrt{26.25}a=26.25​

STEP 9

Take the square root of the result to find the length of the missing side.a=5.12a =5.12a=5.12The length of the missing side of the triangle is approximately5.12, rounded to the nearest hundredth.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the missing side of a right triangle with sides 6.5 and 4. Round your answer to the nearest hundredth. Use $a^2 + b^2 = c^2$ .

We can use the Pythagorean theorem to find the length of the missing side. The theorem is written as follows $c^2 = a^2 + b^2$ where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

We can rearrange the Pythagorean theorem to solve for the missing side (let's call it a):
$a = \sqrt{c^2 - b^2}$

Now, plug in the given values for the hypotenuse (c) and the known leg (b) to calculate the length of the missing side (a).
$a = \sqrt{6.5^2 -4^2}$

Calculate the square of each side.
$a = \sqrt{42.25 -16}$

Subtract the square of the known leg from the square of the hypotenuse.
$a = \sqrt{26.25}$

Take the square root of the result to find the length of the missing side.
$a =5.12$ The length of the missing side of the triangle is approximately5.12, rounded to the nearest hundredth.