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.
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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