Find the Hypotenuse 2

Question 1 of 4

Find the hypotenuse of this triangle.

(15) cm

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Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

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

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

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.

$c = x$ $c=x$

$a = 9$ $a=9$ cm

$b = 12$ $b=12$ cm

${\color{#00880a}{c}}^2$	$=$ $=$	${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$	Pythagoras’ Theorem
${\color{#00880a}{x}}^2$	$=$ $=$	${\color{#9a00c7}{9}}^2 + {\color{#007DDC}{12}}^2$
$x^{2}$ $x^2$	$=$ $=$	$81 + 144$ $81+144$
$x^{2}$ $x^2$	$=$ $=$	$225$ $225$
$\sqrt{x^{2}}$ $sqrt(x^2)$	$=$ $=$	$\sqrt{225}$ $sqrt225$	Get the square root of both sides
$x$ $x$	$=$ $=$	$15$ $15$ cm

15

$15$ cm

Question 2 of 4

Find the hypotenuse of this triangle.

(50) m

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Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

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

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

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.

$c = t$ $c=t$

$a = 14$ $a=14$ m

$b = 48$ $b=48$ m

${\color{#00880a}{c}}^2$	$=$ $=$	${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$	Pythagoras’ Theorem
${\color{#00880a}{t}}^2$	$=$ $=$	${\color{#9a00c7}{14}}^2 + {\color{#007DDC}{48}}^2$
$t^{2}$ $t^2$	$=$ $=$	$196 + 2304$ $196+2304$
$t^{2}$ $t^2$	$=$ $=$	$2500$ $2500$
$\sqrt{t^{2}}$ $sqrt(t^2)$	$=$ $=$	$\sqrt{2500}$ $sqrt2500$	Get the square root of both sides
$t$ $t$	$=$ $=$	$50$ $50$ m

50

$50$ m

Question 3 of 4

Find the hypotenuse of this triangle.

(73) mm

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Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

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

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

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.

$c = t$ $c=t$

$a = 48$ $a=48$ mm

$b = 55$ $b=55$ mm

${\color{#00880a}{c}}^2$	$=$ $=$	${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$	Pythagoras’ Theorem
${\color{#00880a}{t}}^2$	$=$ $=$	${\color{#9a00c7}{48}}^2 + {\color{#007DDC}{55}}^2$
$t^{2}$ $t^2$	$=$ $=$	$2304 + 3025$ $2304+3025$
$t^{2}$ $t^2$	$=$ $=$	$5329$ $5329$
$\sqrt{t^{2}}$ $sqrt(t^2)$	$=$ $=$	$\sqrt{5329}$ $sqrt5329$	Get the square root of both sides
$t$ $t$	$=$ $=$	$73$ $73$ mm

73

$73$ mm

Question 4 of 4

Solve for

y

$y$ .

Round off answer to

1

$1$ decimal place

(12.8)cm

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Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

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

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

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.

$c = y$ $c=y$

$a = 8$ $a=8$ cm

$b = 10$ $b=10$ cm

${\color{#00880a}{c}}^2$	$=$ $=$	${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$	Pythagoras’ Theorem
${\color{#00880a}{y}}^2$	$=$ $=$	${\color{#9a00c7}{8}}^2 + {\color{#007DDC}{10}}^2$
$y^{2}$ $y^2$	$=$ $=$	$64 + 100$ $64+100$
$y^{2}$ $y^2$	$=$ $=$	$164$ $164$
$\sqrt{y^{2}}$ $sqrt(y^2)$	$=$ $=$	$\sqrt{164}$ $sqrt164$	Get the square root of both sides
$y$ $y$	$=$ $=$	$12.8062$ $12.8062$ cm
$y$ $y$	$=$ $=$	$12.8$ $12.8$ cm	Round off to $1$ $1$ decimal place

12.8

$12.8$ cm

Find the Hypotenuse 2

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Quiz summary

Information

1. Question

Hint

Fantastic!

Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

2. Question

Hint

Excellent!

Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

3. Question

Hint

Nice Job!

Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

4. Question

Hint

Fantastic!

Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

Quizzes

Find the Hypotenuse 2

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Quiz summary

Information

1. Question

Hint

Fantastic!

Finding the Hypo+\large\textbf{+}enuse

Use +\large\textbf{+}

2. Question

Hint

Excellent!

Finding the Hypo+\large\textbf{+}enuse

Use +\large\textbf{+}

3. Question

Hint

Nice Job!

Finding the Hypo+\large\textbf{+}enuse

Use +\large\textbf{+}

4. Question

Hint

Fantastic!

Finding the Hypo+\large\textbf{+}enuse

Use +\large\textbf{+}

Quizzes

Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$

Finding the Hypo $\large\textbf{+}$ enuse

Use $\large\textbf{+}$