Years
>
Year 9>
Pythagoras Theorem>
Pythagoras Theorem Mixed Review>
Pythagoras Theorem Mixed Review 4Pythagoras Theorem Mixed Review 4
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- Answered
- Review
-
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)`
Correct
Correct!
Incorrect
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!
Incorrect
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
Help VideoCorrect
Well Done!
Incorrect
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
Help VideoCorrect
Nice Job!
Incorrect
Method OneFinding 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)`
Quizzes
- Find the Hypotenuse 1
- Find the Hypotenuse 2
- Find the Hypotenuse 3
- Find a Side 1
- Find a Side 2
- Find a Side 3
- Pythagoras Problems 1
- Pythagoras Problems 2
- Pythagoras Problems 3
- Pythagoras Theorem Mixed Review 1
- Pythagoras Theorem Mixed Review 2
- Pythagoras Theorem Mixed Review 3
- Pythagoras Theorem Mixed Review 4