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Question 1 of 4
1. Question
Find the value of the missing length `c``a = 30.9` `b=27.9` `c=?`The given measurements are in unitsRound your answer to one decimal place- `c=` (41.6)` \text(units)`
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Pythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` are the two sides, and `c` is the hypotenuseUse the Pythagorean Theorem Formula to solve for `c``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `30.9^2``+``27.9^2` `=` `c^2` Plug in the known lengths `954.81+778.41` `=` `c^2` Evaluate `sqrt(c^2)` `=` `sqrt1733.22` Take the square root of both sides `c` `=` `41.6 \text(units)` Rounded to one decimal place `c=41.6 \text(units)` -
Question 2 of 4
2. Question
Find the value of the missing length `c``a = 3.5` `b=3.7` `c=?`The given measurements are in unitsRound your answer to one decimal place- `c=` (5.1)` \text(units)`
Correct
Great Work!
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Pythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` are the two sides, and `c` is the hypotenuseUse the Pythagorean Theorem Formula to solve for `c``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `3.5^2``+``3.7^2` `=` `c^2` Plug in the known lengths `12.25+13.69` `=` `c^2` Evaluate `sqrt(c^2)` `=` `sqrt25.94` Take the square root of both sides `c` `=` `5.1 \text(units)` Rounded to one decimal place `c=5.1 \text(units)` -
Question 3 of 4
3. Question
One wall is `16 m` tall while the other is `10 m` tall. They stand `8m` apart on a horizontal ground. A roof rests on top of both walls. Find the length of the roof.
- `c=` (10)` \text(m)`
Hint
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Pythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` are the two sides, and `c` is the hypotenuseLabelling each length of the triangle
First, notice that the horizontal ground measuring `8 \text(m)` is the same length as the horizontal side of the triangle.`a` `=` `8` Next, find the length of the side `b`. Do this by subtracting the lengths of the walls.`b` `=` `16-10` `b` `=` `6` Finally, use the Pythagorean Theorem Formula to solve for `c``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `8^2``+``6^2` `=` `c^2` Plug in the known lengths `64+36` `=` `c^2` Evaluate `sqrt(c^2)` `=` `sqrt100` Take the square root of both sides `c` `=` `10 \text(m)` `c=10 \text(m)` -
Question 4 of 4
4. Question
A thin piece of wire `41` metres long is attached to the top of a flag pole. The other end is fixed to the ground at a distance of `15` metres from the base of the flag pole. Find the height of the flag pole.
The given measurements are in metresRound your answer to 2 decimal places- `h=` (38.16)` \text(m)`
Hint
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Method One
Finding a Side
Use $$\large\textbf{-}$$
$${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$$Labelling each length of the triangle
Use the formula for Finding a Side to solve for `h`$${\color{#9a00c7}{a}}^2$$ `=` $${\color{#00880a}{c}}^2-{\color{#007DDC}{b}}^2$$ Finding a Side $${\color{#9a00c7}{h}}^2$$ `=` $${\color{#00880a}{41}}^2-{\color{#007DDC}{15}}^2$$ Plug in the known lengths `h^2` `=` `1681-225` Evaluate `h^2` `=` `1456` `sqrt(h^2)` `=` `sqrt1456` Take the square root of both sides `h` `=` `38.16 \text(m)` Rounded to two decimal places `h=38.16 \text(m)`Method TwoPythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` can be switched as they are both sidesLabelling each length of the triangle
Use the Pythagorean Theorem Formula to solve for `h``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `h^2``+``15^2` `=` `41^2` Plug in the known lengths `h^2+225` `=` `1681` Evaluate `h^2+225` `-225` `=` `1681` `-225` Subtract `225` from both sides `h^2``+225` `-225` `=` `1456` `225-225` cancels out `sqrt(h^2)` `=` `sqrt1456` Take the square root of both sides `h` `=` `38.16 \text(m)` Rounded to two decimal places `h=38.16 \text(m)`