Question

5.8 special right triangles worksheet
name:
1.
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Explanation:

Problem 1

Step1: Identify 45-45-90 triangle

Legs are equal: $w = 4$

Step2: Calculate hypotenuse $y$

$y = 4\sqrt{2}$

Problem 2

Step1: Identify 30-60-90 triangle

Short leg = 2, find long leg $w$
$w = 2\sqrt{3}$

Step2: Calculate hypotenuse $y$

$y = 2 \times 2 = 4$

Problem 3

Step1: Identify 45-45-90 triangle

Hypotenuse $=6\sqrt{2}$, find leg $w$
$w = \frac{6\sqrt{2}}{\sqrt{2}} = 6$

Step2: Legs are equal: $y = w$

$y = 6$

Problem 4

Step1: Identify 30-60-90 triangle

Hypotenuse =10, find short leg $y$
$y = \frac{10}{2} = 5$

Step2: Calculate long leg $w$

$w = 5\sqrt{3}$

Problem 5

Step1: Identify 30-60-90 triangle

Long leg $=5\sqrt{3}$, find short leg $w$
$w = \frac{5\sqrt{3}}{\sqrt{3}} = 5$

Step2: Calculate hypotenuse $y$

$y = 2 \times 5 = 10$

Problem 6

Step1: Identify 45-45-90 triangle

Hypotenuse $=7\sqrt{2}$, find leg $w$
$w = \frac{7\sqrt{2}}{\sqrt{2}} = 7$

Step2: Legs are equal: $y = w$

$y = 7$

Answer:

1. $w=4$, $y=4\sqrt{2}$
2. $w=2\sqrt{3}$, $y=4$
3. $w=6$, $y=6$
4. $w=5\sqrt{3}$, $y=5$
5. $w=5$, $y=10$
6. $w=7$, $y=7$