Pythagoras Problems 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 5 questions completed
Questions:
 1
 2
 3
 4
 5
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
 5
 Answered
 Review

Question 1 of 5
1. Question
Solve for `c`.Round off answer to `1` decimal place (10.8)cm
Hint
Help VideoCorrect
Great Work!
Incorrect
Finding 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.First, find the missing values of the rectangle.Remember that opposite sides of a rectangle are equal.Choose one triangle from the rectangle and label the values. Then substitute them into Pythagoras’ Theorem.`c``=?``a=6` cm`b=9` cm$${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{6}}^2 + {\color{#007DDC}{9}}^2$$ `c^2` `=` `36+81` `c^2` `=` `117` `sqrt(c^2)` `=` `sqrt117` Get the square root of both sides `c` `=` `10.817` cm `c` `=` `10.8` cm Round off to `1` decimal place `10.8` cm 
Question 2 of 5
2. Question
Find the height (`h`) of the ramp.Round off answer to `1` decimal place (2.3)m
Hint
Help VideoCorrect
Correct!
Incorrect
Finding a Side
Use $$\large\textbf{}$$
$${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$$The longest side of a right triangle is called a hypotenuse (`c`). It is also the side opposite the right angle.The height of the ramp (`h`) is a side of a right triangle.Label the values, and then substitute them into Pythagoras’ Theorem (side).`c=13` m`a=h``b=12.8` m$${\color{#9a00c7}{a}}^2$$ `=` $${\color{#00880a}{c}}^2{\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#9a00c7}{h}}^2$$ `=` $${\color{#00880a}{13}}^2{\color{#007DDC}{12.8}}^2$$ `h^2` `=` `169163.84` `h^2` `=` `5.16` `sqrt(h^2)` `=` `sqrt5.16` Get the square root of both sides `h` `=` `2.27156…` m `h` `=` `2.3` m Round off to `1` decimal place `2.3` m 
Question 3 of 5
3. Question
Jack is holding his kite `1.3` meters above the ground. Using the illustration below, find out how high the kite is above the ground.Round off answer to `1` decimal place (35.9)m
Hint
Help VideoCorrect
Fantastic!
Incorrect
Finding a Side
Use $$\large\textbf{}$$
$${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$$The longest side of a right triangle is called a hypotenuse (`c`). It is also the side opposite the right angle.First, find the value of side `h`.Label the values, and then substitute them into Pythagoras’ Theorem (side).`c=41` m`a=h``b=22` m$${\color{#9a00c7}{a}}^2$$ `=` $${\color{#00880a}{c}}^2{\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#9a00c7}{h}}^2$$ `=` $${\color{#00880a}{41}}^2{\color{#007DDC}{22}}^2$$ `h^2` `=` `1681484` `h^2` `=` `1197` `sqrt(h^2)` `=` `sqrt1197` Get the square root of both sides `h` `=` `34.59768` m `h` `=` `34.6` m Round off to `1` decimal place Finally, add `1.3` meters to the length of side `h`.`34.6+1.3` `=` `35.9` m Therefore, the kite is `35.9` meters above the ground.`35.9` m 
Question 4 of 5
4. Question
A `9`metre tree and a `40`metre tree are `23` metres apart. Find the distance between the tips of the two trees (`y`).Round off answer to `1` decimal place (38.6)m
Hint
Help VideoCorrect
Nice Job!
Incorrect
Finding 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.First, draw and label the right triangle made by the two trees.Next, find the value of side `b` by subtracting the height of the smaller tree from the height of the taller tree.`b` `=` `409` `=` `31` m Finally, find the value of `y` by substituting the known values into Pythagoras’ Theorem.`c=y``a=23` m`b=31` m$${\color{#00880a}{c}}^2$$ `=` $${\color{#9a00c7}{a}}^2 + {\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#00880a}{y}}^2$$ `=` $${\color{#9a00c7}{23}}^2 + {\color{#007DDC}{31}}^2$$ `y^2` `=` `529+961` `y^2` `=` `1490` `sqrt(y^2)` `=` `sqrt1490` Get the square root of both sides `y` `=` `38.60051…` m `y` `=` `38.6` m Round off to `1` decimal place `38.6` m 
Question 5 of 5
5. Question
Solve for `h`.Round off answer to `2` decimal places (25.48)cm
Hint
Help VideoCorrect
Great Work!
Incorrect
Finding a Side
Use $$\large\textbf{}$$
$${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$$The longest side of a right triangle is called a hypotenuse (`c`). It is also the side opposite the right angle.First, find the length of one of the sides of the right triangle by subtracting `14` from `38`. Label this side as `b`.`b` `=` `3814` `=` `24` cm Finally, substitute the known values to Pythagoras’ Theorem (side).`c=35` cm`a=h``b=28` cm$${\color{#9a00c7}{a}}^2$$ `=` $${\color{#00880a}{c}}^2{\color{#007DDC}{b}}^2$$ Pythagoras’ Theorem $${\color{#9a00c7}{h}}^2$$ `=` $${\color{#00880a}{35}}^2{\color{#007DDC}{28}}^2$$ `h^2` `=` `1225576` `h^2` `=` `649` `sqrt(h^2)` `=` `sqrt649` Get the square root of both sides `h` `=` `25.4754…` cm `h` `=` `25.48` cm Round off to `2` decimal places `25.48` cm