Question

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45°-45°-90°
special right δ

• leg = ( x )
• hypotenuse = ( xsqrt{2} )

practice find the value of each missing variable.
1.
( x = )
( y = )
2.
( x = )
( y = )
3.
( x = )
( y = )
30°-60°-90°
special right δ

• shorter leg = ( x )
• longer leg = ( xsqrt{3} )
• hypotenuse = ( 2x )

practice find the value of each missing variable.
4.
( x = )
( y = )
5.
( x = )
( y = )
6.
( x = )
( y = )
7.
( x = )
( y = )
8.
( x = )
( y = )
9.
( x = )
( y = )

Explanation:

45°-45°-90° Special Right Triangle Problems

Step1: Recall 45-45-90 ratios

Leg $= x$, Hypotenuse $= x\sqrt{2}$
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Problem 1:

Step1: Identify leg length

Leg $x = 8$

Step2: Calculate hypotenuse $y$

$y = 8\sqrt{2}$
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Problem 2:

Step1: Isolate leg $x$

Hypotenuse $25\sqrt{2}=x\sqrt{2} \implies x=25$

Step2: Equal legs, so $y=x$

$y=25$
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Problem 3:

Step1: Calculate leg $x$

Hypotenuse $19=x\sqrt{2} \implies x=\frac{19}{\sqrt{2}}=\frac{19\sqrt{2}}{2}$

Step2: Equal legs, so $y=x$

$y=\frac{19\sqrt{2}}{2}$

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30°-60°-90° Special Right Triangle Problems

Step1: Recall 30-60-90 ratios

Shorter leg $= x$, Longer leg $= x\sqrt{3}$, Hypotenuse $= 2x$
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Problem 4:

Step1: Identify shorter leg $x$

Shorter leg $x=5$

Step2: Calculate hypotenuse $y$

$y=2x=10$
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Problem 5:

Step1: Identify longer leg, find $x$

Longer leg $14=x\sqrt{3} \implies x=\frac{14\sqrt{3}}{3}$

Step2: Calculate hypotenuse $y$

$y=2x=\frac{28\sqrt{3}}{3}$
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Problem 6:

Step1: Identify shorter leg $x$

Shorter leg $x=16$

Step2: Calculate longer leg $y$

$y=16\sqrt{3}$
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Problem 7:

Step1: Identify hypotenuse, find $x$

Hypotenuse $46=2x \implies x=23$

Step2: Calculate longer leg $y$

$y=23\sqrt{3}$
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Problem 8:

Step1: Identify hypotenuse, find $x$

Hypotenuse $20=2x \implies x=10$

Step2: Calculate longer leg $y$

$y=10\sqrt{3}$
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Problem 9:

Step1: Identify hypotenuse, find $x$

Hypotenuse $6=2x \implies x=3$

Step2: Calculate longer leg $y$

$y=3\sqrt{3}$

Answer:

45°-45°-90° Problems

1. $x=8$, $y=8\sqrt{2}$
2. $x=25$, $y=25$
3. $x=\frac{19\sqrt{2}}{2}$, $y=\frac{19\sqrt{2}}{2}$

30°-60°-90° Problems

1. $x=5$, $y=10$
2. $x=\frac{14\sqrt{3}}{3}$, $y=\frac{28\sqrt{3}}{3}$
3. $x=16$, $y=16\sqrt{3}$
4. $x=23$, $y=23\sqrt{3}$
5. $x=10$, $y=10\sqrt{3}$
6. $x=3$, $y=3\sqrt{3}$