Special Right Triangles: 45-45-90 and 30-60-90

Grade 10·21 problems·~35 min·Digital SAT Math·topic·sat-geotrig-rt-special

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Recall / Warm-Up

What is the ratio of sides in a 45-45-90 triangle (leg : leg : hypotenuse)?

$1:1:2$

$1:1:\\sqrt{2}$

$1:\\sqrt{3}:2$

$1:2:\\sqrt{3}$

In a 30-60-90 triangle, which side is opposite the 30° angle?

The hypotenuse

The long leg

The short leg

All sides are equal

A right isosceles triangle has both legs equal to 1. Use the Pythagorean theorem
to find the exact length of the hypotenuse.

Enter your answer using radical notation (e.g., sqrt(2)).

A 45-45-90 triangle has legs of length 7. Find the length of the hypotenuse. Enter your answer in simplified radical form (e.g., 7*sqrt(2)).

A 45-45-90 triangle has a hypotenuse of 10. Find the length of each leg. Enter your answer in simplified radical form.

A 30-60-90 triangle has its short leg equal to 6. Find the length of the hypotenuse.

A 30-60-90 triangle has its hypotenuse equal to 14. Find the length of the long leg. Enter your answer in simplified radical form.

A 30-60-90 triangle has its long leg equal to $9\sqrt{3}$ .
What is the length of the hypotenuse?

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