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

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Question

What is the length of the remaining side of the right triangle?

Answer

Rearrange the Pythagorean Theorem to find the missing side. The Pythagorean Theorem is:

$c^{2}=a^{2}+b^{2}$

where is the hypotenuse and and are the sides.

$\sqrt{(15^{2}-9^{2})} = 12$

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Question

Find the length of the unknown side, , of the right triangle below.

Answer

We need to use the Pythagorean Theorem, which says that .

Since we need to find the length of 'a', we can just solve for 'a'.

$a=\sqrt{c^2-b^2}$

In our case, c = 12 and b = 9.

Thus, $a=\sqrt{12^2-9^2}=\sqrt{144-81}=\sqrt{63}=\sqrt{9 \cdot 7}=\sqrt{9}\sqrt{7}=3\sqrt7$ .

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Question

The hypotenuse of a right triangle is 26 in and one leg is 10 in. What is the sum of the two shortest sides?

Answer

We use the Pythagorean Theorem so the problem to solve becomes $10^{2}+x^{2}=26^{2}$ where = unknown leg length

So $100 + x^{2}=676$ and

The sum of the two legs becomes

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Question

$In;\Delta KLM,;what;is;the;length;of;\overline{KL}?$

Answer

$\fn_cm A^2+4^2=5^2$

$A=\sqrt9$

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Question

Find the missing leg of the right triangle when one of the legs is and the hypotenuse is .

Answer

In order to find the missing side of a right triangle you must use one of two things:

1. Pythagorean Theorem

2. Trigonometry.

Since we only know what the side lengths are we must use the Pythagorean Theorem.

a=4, b=x, and c=5

So the missing side length is 3

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Question

Given that the hypotenuse of a right triangle is and one side is , find the other side length.

Answer

To find the length of the missing side, you can either use the pythagorean theorm or realize this is a case of a special right triangle with sides .

Thus, the other side length is .

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{22^2-8^2}=\sqrt{420}=20.49$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{22^2-p^2}=\sqrt{403}=20.07$

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Question

Find the length of the missing side length.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{22^2-10^2}=\sqrt{384}=19.60$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{25^2-5^2}=\sqrt{600}=24.49$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{25^2-10^2}=\sqrt{525}=22.91$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{25^2-12^2}=\sqrt{481}=21.93$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{25^2-15^2}=\sqrt{400}=20$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{18^2-3^2}=\sqrt{315}=17.75$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{18^2-7^2}=\sqrt{275}=16.58$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{18^2-9^2}=\sqrt{243}=15.59$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{18^2-6^2}=\sqrt{288}=16.97$

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Question

Find the length of the missing side.

Answer

Recall the Pythagorean Theorem for a right triangle:

Since the missing side corresponds to side , rewrite the Pythagorean Theorem and solve for .

$b=\sqrt{c^2-a^2}$

Now, plug in values of and into a calculator to find the length of side . Round to decimal places.

$b=\sqrt{17^2-8^2}=\sqrt{225}=15$

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Question

Given the right triangle above, find the value of .

Answer

To find the length of the side x, we must use the Pythagorean Theorem

.

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.

So, when we plug the given values into the formula, the equation looks like

which can be simplified to

.

Next, solve for b and we get a final answer of

$b=\sqrt{9}=3$ .

This particular example is a Pythagorean triple, or a right triangle with 3 whole number values, so it is a good one to remember.

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Question

Given the right triangle above, find the length of the missing side.

Answer

To find the length of the side x, we must use the Pythagorean Theorem

.

However, this time since we are given the value of the hypotenuse, we will solve for side b rather than c.

So, when we plug the given values into the formula, the equation looks like

which can be simplified to

.

Next, solve for b and we get a final answer of

$b=\sqrt{1600}=40$ .

This particular example is a Pythagorean triple, or a right triangle with 3 whole number values, so it is a good one to remember.

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