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Math  /  Geometry

QuestionWhat is the length of the missing leg? If necessary, round to the nearest tenth. b=b= □\square centimeters Submit

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. We are given one leg and the hypotenuse.
3. We need to find the length of the missing leg b b .

STEP 2

1. Use the Pythagorean Theorem to set up an equation.
2. Solve for the missing leg b b .
3. Round the result to the nearest tenth if necessary.

STEP 3

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. This can be written as:
a2+b2=c2 a^2 + b^2 = c^2
where a a and b b are the legs, and c c is the hypotenuse.

STEP 4

Substitute the known values into the Pythagorean Theorem. Here, a=3 a = 3 cm and c=7 c = 7 cm:
32+b2=72 3^2 + b^2 = 7^2

STEP 5

Calculate the squares of the known values:
9+b2=49 9 + b^2 = 49

STEP 6

Isolate b2 b^2 by subtracting 9 from both sides:
b2=49−9 b^2 = 49 - 9 b2=40 b^2 = 40

STEP 7

Take the square root of both sides to solve for b b :
b=40 b = \sqrt{40}

STEP 8

Simplify the square root if possible and round to the nearest tenth:
b=40 b = \sqrt{40} b≈6.3 b \approx 6.3
The length of the missing leg b b is approximately:
6.3 \boxed{6.3} centimeters

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