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

Grade 10·22 problems·~37 min·Digital SAT Math·topic·sat-geotrig-rt-special

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Recall / Warm-Up

An isosceles triangle has two equal sides that meet at a $120\degree$ angle. What is the measure of each of the other two angles?

$30\degree$

$60\degree$

$120\degree$

$15\degree$

Which expression is equal to $\dfrac{10}{\sqrt{2}}$ ?

$10\sqrt{2}$

$5\sqrt{2}$

$5$

$\dfrac{5\sqrt{2}}{2}$

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 (for example, write sqrt(5) for $\sqrt{5}$ ).

A 45-45-90 triangle has legs of length 7. Find the length of the hypotenuse. Enter your answer in simplified radical form (for example, 3*sqrt(5)).

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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