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imlittlestar

Answer:

The length of a leg of the triangle = 59.83 cm

Step-by-step explanation:

Points to remember

If a right angled triangle with angles 45°, 45° and 90° then the sides are in ratio 1 : 1 : √2

It is given a right angled triangle with  45°, 45° and 90° and hypotenuse = 84.6 cm

To find the length of a leg

Let 'x' be the length of each leg,

From the figure we can write,

1: 1 :  √2 = x : x : 84.6

Therefore x = 84.6/√2

 = 59.83 cm

Therefore the length of a leg of the triangle = 59.83 cm

kudzordzifrancis

ANSWER

59.82

EXPLANATION

The given right angle is an isosceles right triangle.

Let the length of a leg be x cm.

Then by the Pythagoras Theorem,

[tex] {x}^{2} + {x}^{2} = 84.6 ^{2} [/tex]

[tex]2 {x}^{2} = 7157.16[/tex]

Divide both sides by 2.

[tex]{x}^{2} = \frac{7157.16}{2} [/tex]

[tex]{x}^{2} = 3578.58[/tex]

Take positive square root of both sides to get,

[tex]x = 59.82123369[/tex]

Hence the length of a leg is 59.82 to the nearest hundredth.