The length of the hypotenuse of a 45°-45°-90° triangle is 12 units. Find the exact value of the length of the leg.

The length of the hypotenuse of a 30°-60°-90° triangle is 14 units. Find the exact value of the length of the short leg.

1.

This is an isosceles right-angled triangle

Let unknown equal sides be x and x

Using Pythagoras x² + x² = 12²

2x² = 144

x² = 72

x = √72 exactly

or simplified x = 6√2

2. note that in a 30°-60°-90° triangle the sides are in the rarios

1: √3 : 2 (smallest to biggest)

= 7: 7√3 : 14 (multiplying by 7)

So smallest side = 7 units exactly

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