QZ #15 Review Pythagorean Theorem

Find the length of the missing side.

• 17 cm

• 22 cm

• 15 cm

• 13 cm

Answer explanation

$c=\sqrt{a^2+b^2\ }=\sqrt{5^2+12^2\ }=13\ cm$

^{Find the missing side.}

• 48

• 108

• 83.6

• 72

Answer explanation

$b=\sqrt{c^2-a^2}=\sqrt{78^2-30^2}=72$

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

what is the missing length?

• 50

• 60

• 70

• 80

Answer explanation

$c=\sqrt{a^2+b^2}=\sqrt{30^2+40^2}=50$

What is the distance between the two points?

• 6.3

• 6.5

• 6.7

• 16

Answer explanation

Method 1:Form a right triangle, and count the lengths of the two legs. $c=\sqrt{a^2+b^2}=\sqrt{6^2+2^2}\approx6.3$

Method 2: Label the coordinates, and use the big formula.

$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}=\sqrt{\left(4--2\right)^2+\left(3-1\right)^2}\approx6.3$

What is the distance between the points? Round up to the nearest tenth, if needed.

• 6.2

• 5.7

• 6

• 5.8

Answer explanation

Method 1:Form a right triangle, and count the lengths of the two legs. $c=\sqrt{a^2+b^2}=\sqrt{3^2+5^2}\approx5.8$

Method 2: Label the coordinates, and use the big formula.
$d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}=\sqrt{\left(4-1\right)^2+\left(5-0\right)^2}\approx5.8$

In a right triangle, if a = 8 and c = 17, what is the correct setup to find the value of b?

• $17^2+8^2=b^2$

• $8^2+b^2=17^2$

• $17^2+b^2=8^2$

• $\frac{8^2}{b^2}=\frac{17^2}{100}$

The longest side of a right triangle is DIRECTLY ACROSS from the...

• right angle.
• acute angle.
• obtuse angle.

What is the final step in solving this work for c?
a² + b² = c²
3² + 4² = c²
9 + 16 = c²
25 = c²

• Divide both sides by 2
• Take the square root of both sides

Find the missing side.

• 36

• 76.8

• 12

• 40

Answer explanation

 $a=\sqrt{c^2-b^2}=$   $\sqrt{60^2-48^2}=36$