Question

The area of a right triangle is 50. One of its angles is 45°. Find the lengths of the sides and hypotenuse of the triangle.​

Answer 1

Answer:

The triangle is right and the size one of its angles is 45°; the third angle has a size 45° and therefore the triangle is right and isosceles. Let x be the length of one of the sides and H be the length of the hypotenuse.

Area = (1/2)x2 = 50 , solve for x: x = 10

We now use Pythagora to find H: x2 + x2 = H2

Solve for H: H = 10 √(2)

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Answer 2

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The triangle is right and the size one of its angles is 45°; the third angle has a size 45° and therefore the triangle is right and isosceles. Let x be the length of one of the sides and H be the length of the hypotenuse.

Area = (1/2)x2 = 50 , solve for x: x = 10

We now use Pythagora to find H: x2 + x2 = H2

Solve for H: H = 10 √(2)