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Anonymous asked in Science & MathematicsMathematics · 1 month ago

# A 45-45-90 triangle has a hypotenuse with a length of 10 ft. What are the lengths of the other legs?

What are the lengths of the other legs?

A)9.14 ft

B)7.07 ft

C)8.46 ft

D)6.36 ft

Relevance

45-45-90 triangle is an isosceles triangle. Therefore, it will have 2 equal sides.

Let the equal sides be xFor a right-angled triangle, by Pythagoras Theorem,x^2 + x^2 = 10^2

2x^2 = 100

x^2 = 50

x = 7.07       (since x > 0)

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• =sqrt((10*10)/2)=sqrt(50)=7.07 ft  B.

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• x²  +  x²   =  10²

2 x²   = 100

x²   =  50

x   = 5 √2

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• Let x be the leg length.

sin45 = x/10

0.707 = x/10

x = 7.07 ft

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• Using Pythagoras' theorem the other legs are 7.07 ft which is option B)

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• It is an isosceles triangle. The base is the hypotenuse. The other sides will be equal to each other.

Pythagoras:

a^2 + b^2 = h^2

a^2 + b^2 = 10^2

but a = b, so substitute:

b^2 + b^2 = 10^2

2b^2 = 100

b^2 = 50

b = 7.07

ANS (B)

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• A 45°–45°–90° triangle has a hypotenuse with a length of 10 ft.

What are the lengths of the other legs?

n√2 = 10 feet

n = 7.071067812 feet

B) 7.07 ft

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• There are a couple of ways to do this.

The most basic way is to apply the Pythagorean Theorem.

A-squared + B-squared = C-squared

since A and B are the same in the triangle described

2(A-squared) = C-squared

2(A-squared) = 10 squared

2(A-squared) = 100

A-squared = 50

A = sqrt(50)

which

I'd guess

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