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

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

Work through problems with immediate feedback

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?

You're viewing 2 of 6 sections.

Create a free account to continue the full exercise set and save your progress.

0 of 8 answered

Answer all problems to submit.