Math / Geometry

QuestionSides $a$ and $b$ represent the two legs of a right triangle, and c represents the hypotenuse. Find the length of the unknown side. $a=14 \text { in., } c=50 \text { in. }$
The length of the third side is $\square$ $\square$ (Simplify your answer. Type an exact answer, using radicals as needed.)

Studdy Solution

STEP 1

What is this asking? We're given the lengths of two sides of a right triangle and need to find the length of the missing side! Watch out! Remember, $c$ is always the hypotenuse, the longest side, in the Pythagorean theorem.

STEP 2

1. Set up the Pythagorean Theorem
2. Solve for the unknown side

STEP 3

Alright, let's kick things off with the famous Pythagorean Theorem: $a^2 + b^2 = c^2$ .
This tells us how the sides of a right triangle relate to each other.

STEP 4

We know that $a = 14$ in. and $c = 50$ in.
Let's plug these values into our equation: $(14)^2 + b^2 = (50)^2$

STEP 5

Time to crunch some numbers!
Squaring both $(14)$ and $(50)$ gives us: $196 + b^2 = 2500$ Remember, $14 \cdot 14 = 196$ and $50 \cdot 50 = 2500$ .

STEP 6

Now, let's get $b^2$ by itself.
We can do this by subtracting $196$ from both sides of the equation: $196 - 196 + b^2 = 2500 - 196$ $b^2 = 2304$

STEP 7

Almost there!
To find $b$ , we need to take the square root of both sides: $\sqrt{b^2} = \sqrt{2304}$ $b = 48$ So, the length of the missing side, $b$ , is 48 inches!

STEP 8

The length of the unknown side is $48$ inches.

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Studdy Solution

STEP 1

What is this asking? We're given the lengths of two sides of a right triangle and need to find the length of the missing side! Watch out! Remember, $c$ is always the hypotenuse, the longest side, in the Pythagorean theorem.

STEP 2

1. Set up the Pythagorean Theorem
2. Solve for the unknown side

STEP 3

Alright, let's kick things off with the famous Pythagorean Theorem: $a^2 + b^2 = c^2$ .
This tells us how the sides of a right triangle relate to each other.

STEP 4

We know that $a = 14$ in. and $c = 50$ in.
Let's plug these values into our equation: $(14)^2 + b^2 = (50)^2$

STEP 5

Time to crunch some numbers!
Squaring both $(14)$ and $(50)$ gives us: $196 + b^2 = 2500$ Remember, $14 \cdot 14 = 196$ and $50 \cdot 50 = 2500$ .

STEP 6

Now, let's get $b^2$ by itself.
We can do this by subtracting $196$ from both sides of the equation: $196 - 196 + b^2 = 2500 - 196$ $b^2 = 2304$

STEP 7

Almost there!
To find $b$ , we need to take the square root of both sides: $\sqrt{b^2} = \sqrt{2304}$ $b = 48$ So, the length of the missing side, $b$ , is 48 inches!

STEP 8

The length of the unknown side is $48$ inches.

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Studdy Solution

STEP 1

What is this asking? We're given the lengths of two sides of a right triangle and need to find the length of the missing side! Watch out! Remember, ccc is *always* the hypotenuse, the longest side, in the Pythagorean theorem.

STEP 2

1. Set up the Pythagorean Theorem2. Solve for the unknown side

STEP 3

Alright, let's **kick things off** with the famous Pythagorean Theorem: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2.This tells us how the sides of a right triangle relate to each other.

STEP 4

We know that a=14a = 14a=14 in. and c=50c = 50c=50 in.Let's **plug these values** into our equation: (14)2+b2=(50)2(14)^2 + b^2 = (50)^2(14)2+b2=(50)2

STEP 5

Time to **crunch some numbers**!Squaring both (14)(14)(14) and (50)(50)(50) gives us: 196+b2=2500196 + b^2 = 2500196+b2=2500 Remember, 14⋅14=19614 \cdot 14 = 19614⋅14=196 and 50⋅50=250050 \cdot 50 = 250050⋅50=2500.

STEP 6

Now, let's **get** b2b^2b2 **by itself**.We can do this by subtracting 196196196 from both sides of the equation: 196−196+b2=2500−196196 - 196 + b^2 = 2500 - 196196−196+b2=2500−196 b2=2304b^2 = 2304b2=2304

STEP 7

Almost there!To find bbb, we need to take the **square root** of both sides: b2=2304\sqrt{b^2} = \sqrt{2304}b2​=2304​ b=48b = 48b=48So, the length of the missing side, bbb, is **48 inches**!

STEP 8

The length of the unknown side is 484848 inches.

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Studdy solves anything!

Start learning now

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

What is this asking? We're given the lengths of two sides of a right triangle and need to find the length of the missing side! Watch out! Remember, $c$ is always the hypotenuse, the longest side, in the Pythagorean theorem.

1. Set up the Pythagorean Theorem
2. Solve for the unknown side

Alright, let's kick things off with the famous Pythagorean Theorem: $a^2 + b^2 = c^2$ .
This tells us how the sides of a right triangle relate to each other.

We know that $a = 14$ in. and $c = 50$ in.
Let's plug these values into our equation: $(14)^2 + b^2 = (50)^2$

Time to crunch some numbers!
Squaring both $(14)$ and $(50)$ gives us: $196 + b^2 = 2500$ Remember, $14 \cdot 14 = 196$ and $50 \cdot 50 = 2500$ .

Now, let's get $b^2$ by itself.
We can do this by subtracting $196$ from both sides of the equation: $196 - 196 + b^2 = 2500 - 196$ $b^2 = 2304$

Almost there!
To find $b$ , we need to take the square root of both sides: $\sqrt{b^2} = \sqrt{2304}$ $b = 48$ So, the length of the missing side, $b$ , is 48 inches!

The length of the unknown side is $48$ inches.