MA 410 | Review (Chs 8.2-8.3)

Simplifying Radicals

100

sqrt(75)

5sqrt(3)

200

sqrt(89)

irreducible

300

1/sqrt(2)

sqrt(2)/2

400

9/sqrt(8)

(9sqrt(2))/4

The Pythagorean Theorem

100

Find the hypotenuse of a triangle with side lengths 3 and 5.

sqrt(34)

200

Find the hypotenuse of a triangle with side lengths 6 and 7.

sqrt(85)

300

Find the hypotenuse of a triangle with side lengths 10 and 9.

sqrt(181)

400

Find the hypotenuse of a triangle with side lengths 15 and 22.

sqrt(709)

Side Measures of the Special Right Triangles

100

In a 45-45-90 right triangle, the measure of the side opposite of the 90-degree angle is...

xsqrt(2)

200

In a 30-60-90 right triangle, the formula for the side opposite the 60-degree angle is...

xsqrt(3)

300

In a 30-60-90 right triangle, the formula for the side opposite the 90-degree angle is...

2x

400

Why are there only two formulae that we have to memorize for the side lengths of a 45-45-90 right triangle?

Because a 45-45-90 right triangle is an isosceles right triangle, where two angles and their corresponding opposite sides are congruent.

Solving in a 45-45-90 Right Triangle

100

What is the length of the leg opposite the 45-degree angle of a 45-45-90 right triangle, whose hypotenuse is

5sqrt(2)

5

200

What is the length of the leg opposite the 45-degree angle of a 45-45-90 right triangle, whose hypotenuse is 6.

3sqrt(2)

300

What is the length of the leg opposite the 45-degree angle of a 45-45-90 right triangle, whose hypotenuse is 58.

29sqrt(2)

400

What is the length of the leg opposite the 45-degree angle of a 45-45-90 right triangle, whose hypotenuse is

40sqrt2

40

Solving in a 30-60-90 Right Triangle

100

What is the length of the leg opposite the 60-degree angle of a 30-60-90 right triangle if the length of the leg opposite the 30-degree angle is 12?

12sqrt(3)

200

What is the length of the leg opposite the 30-degree angle of a 30-60-90 right triangle if the length of the leg opposite the 90-degree angle is 7?

7/2

300

What is the length of the leg opposite the 90-degree angle of a 30-60-90 right triangle if the length of the leg opposite the 60-degree angle is 

2sqrt(6)

4sqrt(2)

400

What is the length of the leg opposite the 30-degree angle of a 30-60-90 right triangle if the length of the leg opposite the 60-degree angle is 

2sqrt(6)

2sqrt(2)