f the hypotenuse of a 45°-45°-90° triangle is 13, what is the length of one of the legs? A. 2004-04-01-04-00_files/i0360004.jpg B. 2004-04-01-04-00_files/i0360003.jpg C. 2004-04-01-04-00_files/i0360001.jpg D. 2004-04-01-04-00_files/i0360002.jpg

F the hypotenuse of a 45°-45°-90° triangle is 13.
We can see that this is an isosceles triangle,
and its two legs are equal.
From Pythagorean theorem we can write
(leg)² + (leg)² = (hypotenuse)²
2(leg)²= (hypotenuse)²
2(leg)²= 13²
(leg)² = 13²/2, we need only positive root,
leg = √(13²/2)=13/√2=(13√2)/2 exact value
leg ≈ 9.19 approximate value

Answer Link

vintechnology vintechnology · Answer 2 · 2022-01-26T15:05:01+01:00

The length of one of the leg of a 45°-45°-90° triangle with the hypotenuse side as 13 is 9.19.

Right angle triangle:

A right angle triangle has one its angles as 90 degree. The sides are called hypotenuse , adjacent and opposite side depending on the position of the angle.

Therefore,

Using trigonometric ratios, we can find one of the other legs of the right angle triangle.

sin 45 = opposite / hypotenuse

Hypotenuse side is the longest side of a right angle triangle and it is given as 13. Therefore,

sin 45° = opposite / 13

cross multiply

opposite = 13 sin45°

opposite = 13 × 0.70710678118

opposite side = 9.19238815543

Therefore, one of its leg is approximately 9.19

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