Pythagoras' Theorem
Find the Hypotenuse 1
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Question 1 of 4
1. Question
Find the hypotenuse of this triangle.
- (5) cm
Hint
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Help VideoFinding the Hypo$$\large\textbf{+}$$enuse
Use $$\large\textbf{+}$$
$${\color{#00880a}{c}}^2={\color{#9a00c7}{a}}^2 \hspace{1mm} \large\textbf{+} \hspace{1mm} \normalsize{{\color{#007DDC}{b}}^2}$$The longest side of a right triangle is called a hypotenuse (`c`). It is also the side opposite the right angle.Label the values, and then substitute them into Pythagoras’ Theorem.
`c``=?``a=3` cm`b=4` cm$${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{3}}^2 + {\color{#007DDC}{4}}^2$$ `c^2` `=` `9+16` `c^2` `=` `25` `sqrt(c^2)` `=` `sqrt25` Get the square root of both sides `c` `=` `5` cm `5` cm -
Question 2 of 4
2. Question
Find the hypotenuse of this triangle.
- (13) mm
Hint
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Incorrect
Help VideoFinding the Hypo$$\large\textbf{+}$$enuse
Use $$\large\textbf{+}$$
$${\color{#00880a}{c}}^2={\color{#9a00c7}{a}}^2 \hspace{1mm} \large\textbf{+} \hspace{1mm} \normalsize{{\color{#007DDC}{b}}^2}$$The longest side of a right triangle is called a hypotenuse (`c`). It is also the side opposite the right angle.Label the values, and then substitute them into Pythagoras’ Theorem.
`c``=?``a=5` mm`b=12` mm$${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{5}}^2 + {\color{#007DDC}{12}}^2$$ `c^2` `=` `25+144` `c^2` `=` `169` `sqrt(c^2)` `=` `sqrt169` Get the square root of both sides `c` `=` `13` mm `13` mm -
Question 3 of 4
3. Question
Find the hypotenuse of this triangle.
- (10) m
Hint
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Correct!
Incorrect
Help VideoFinding the Hypo$$\large\textbf{+}$$enuse
Use $$\large\textbf{+}$$
$${\color{#00880a}{c}}^2={\color{#9a00c7}{a}}^2 \hspace{1mm} \large\textbf{+} \hspace{1mm} \normalsize{{\color{#007DDC}{b}}^2}$$The longest side of a right triangle is called a hypotenuse (`c`). It is also the side opposite the right angle.Label the values, and then substitute them into Pythagoras’ Theorem.
`c``=?``a=6` m`b=8` m$${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{6}}^2 + {\color{#007DDC}{8}}^2$$ `c^2` `=` `36+64` `c^2` `=` `100` `sqrt(c^2)` `=` `sqrt100` Get the square root of both sides `c` `=` `10` m `10` m -
Question 4 of 4
4. Question
Find the hypotenuse of this triangle.
- (26) m
Hint
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Keep Going!
Incorrect
Help VideoFinding the Hypo$$\large\textbf{+}$$enuse
Use $$\large\textbf{+}$$
$${\color{#00880a}{c}}^2={\color{#9a00c7}{a}}^2 \hspace{1mm} \large\textbf{+} \hspace{1mm} \normalsize{{\color{#007DDC}{b}}^2}$$The longest side of a right triangle is called a hypotenuse (`c`). It is also the side opposite the right angle.Label the values, and then substitute them into Pythagoras’ Theorem.
`c=x``a=24` m`b=10` m$${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#00880a}{x}}^2$$ `=` $${\color{#9a00c7}{24}}^2 + {\color{#007DDC}{10}}^2$$ `x^2` `=` `576+100` `x^2` `=` `676` `sqrt(x^2)` `=` `sqrt676` Get the square root of both sides `x` `=` `26` m `26` m