Question

mixed practice find the value of each variable.
10.

x = ______
y = ______
11.

x = ______
y = ______
12.

x = ______
y = ______
13.

x = ______
y = ______
14.

x = ______
y = ______
15.

x = ______
y = ______
16.

x = ______
y = ______
17.

x =

y =
18.

x = ______
y = ______
19.

x = ______
y = ______
z = ______
20.

x = ______
y = ______
z = ______
21.

x = ______
y = ______
z = ______
22.

x = ______
y = ______
z = ______
23.

x = ______
y = ______
z = ______
24.

x = ______
y = ______
z = ______
© gina wilson (all things algebra), 2014

Explanation:

Problem 10

Step1: Identify 45-45-90 triangle

In a 45-45-90 triangle, legs are equal, hypotenuse = $leg \times \sqrt{2}$.

Step2: Solve for $x,y$

$x = y = \frac{28}{\sqrt{2}} = 14\sqrt{2}$

Step1: Identify 30-60-90 triangle

Short leg = 16, long leg = $short\ leg \times \sqrt{3}$, hypotenuse = $2 \times short\ leg$.

Step2: Solve for $x,y$

$x = 2 \times 16 = 32$
$y = 16\sqrt{3}$

Step1: Identify 45-45-90 triangle

Leg = 4, legs are equal, hypotenuse = $4\sqrt{2}$.

Step2: Solve for $x,y$

$x = 4$, $y = 4\sqrt{2}$

Answer:

$x = 14\sqrt{2}$, $y = 14\sqrt{2}$

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Problem 11