Find a Side 3

Years

Year 8

Pythagoras Theorem

Find a Side

Find a Side 3

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Time

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Answered
Review

Question 1 of 3

Solve for

x

$x$ .

Round off answer to

1

$1$ decimal place

(7.5)cm

Incorrect

Finding a Side

Use $\large\textbf{-}$

a^{2} = c^{2} - b^{2}

${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$

The longest side of a right triangle is called a hypotenuse (

c

$c$ ). It is also the side opposite the right angle.

Label the values, and then substitute them into Pythagoras’ Theorem (side).

$c = 19.5$ $c=19.5$ cm

$a = x$ $a=x$

$b = 18$ $b=18$ cm

${\color{#9a00c7}{a}}^2$	$=$ $=$	${\color{#00880a}{c}}^2-{\color{#007DDC}{b}}^2$	Pythagoras’ Theorem
${\color{#9a00c7}{x}}^2$	$=$ $=$	${\color{#00880a}{19.5}}^2-{\color{#007DDC}{18}}^2$
$x^{2}$ $x^2$	$=$ $=$	$380.25 - 324$ $380.25-324$
$x^{2}$ $x^2$	$=$ $=$	$56.25$ $56.25$
$\sqrt{x^{2}}$ $sqrt(x^2)$	$=$ $=$	$\sqrt{56.25}$ $sqrt56.25$	Get the square root of both sides
$x$ $x$	$=$ $=$	$7.5$ $7.5$ cm

7.5

$7.5$ cm

Question 2 of 3

Solve for

x

$x$ .

Round off answer to

2

$2$ decimal places

(24.91)m

Incorrect

Finding a Side

Use $\large\textbf{-}$

a^{2} = c^{2} - b^{2}

${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$

The longest side of a right triangle is called a hypotenuse (

c

$c$ ). It is also the side opposite the right angle.

Label the values, and then substitute them into Pythagoras’ Theorem (side).

$c = 30.5$ $c=30.5$ m

$a = x$ $a=x$

$b = 17.6$ $b=17.6$ m

${\color{#9a00c7}{a}}^2$	$=$ $=$	${\color{#00880a}{c}}^2-{\color{#007DDC}{b}}^2$	Pythagoras’ Theorem
${\color{#9a00c7}{x}}^2$	$=$ $=$	${\color{#00880a}{30.5}}^2-{\color{#007DDC}{17.6}}^2$
$x^{2}$ $x^2$	$=$ $=$	$930.25 - 309.76$ $930.25-309.76$
$x^{2}$ $x^2$	$=$ $=$	$620.49$ $620.49$
$\sqrt{x^{2}}$ $sqrt(x^2)$	$=$ $=$	$\sqrt{620.49}$ $sqrt620.49$	Get the square root of both sides
$x$ $x$	$=$ $=$	$24.9096 \dots$ $24.9096…$ cm
$x$ $x$	$=$ $=$	$24.91$ $24.91$ m	Round off to $2$ $2$ decimal places

24.91

$24.91$ m

Question 3 of 3

Solve for

y

$y$ .

Round off answer to

2

$2$ decimal places

(10.33)m

Incorrect

Finding a Side

Use $\large\textbf{-}$

a^{2} = c^{2} - b^{2}

${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$

The longest side of a right triangle is called a hypotenuse (

c

$c$ ). It is also the side opposite the right angle.

Label the values, and then substitute them into Pythagoras’ Theorem (side).

$c = 17$ $c=17$ m

$a = y$ $a=y$

$b = 13.5$ $b=13.5$ m

${\color{#9a00c7}{a}}^2$	$=$ $=$	${\color{#00880a}{c}}^2-{\color{#007DDC}{b}}^2$	Pythagoras’ Theorem
${\color{#9a00c7}{y}}^2$	$=$ $=$	${\color{#00880a}{17}}^2-{\color{#007DDC}{13.5}}^2$
$y^{2}$ $y^2$	$=$ $=$	$289 - 182.25$ $289-182.25$
$y^{2}$ $y^2$	$=$	$106.75$
$sqrt(y^2)$	$=$	$sqrt106.75$	Get the square root of both sides
$y$	$=$	$10.3319$ m
$x$	$=$	$10.33$ m	Round off to $2$ decimal places

$10.33$ m

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Quiz summary

Information

1. Question

Hint

Excellent!

Finding a Side

Use $\large\textbf{-}$

2. Question

Hint

Keep Going!

Finding a Side

Use $\large\textbf{-}$

3. Question

Hint

Great Work!

Finding a Side

Use $\large\textbf{-}$

Quizzes

Find a Side 3

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Quiz summary

Information

1. Question

Hint

Excellent!

Finding a Side

Use --\large\textbf{-}

2. Question

Hint

Keep Going!

Finding a Side

Use --\large\textbf{-}

3. Question

Hint

Great Work!

Finding a Side

Use --\large\textbf{-}

Quizzes

Use $\large\textbf{-}$

Use $\large\textbf{-}$

Use $\large\textbf{-}$