Question

Please help me i would appreciate it so much

1) The sketch below represents the side view of the pavilion. Round all answers off to the nearest two decimal places unless otherwise stated.


2) Calculate the length of AB


3) Calculate the total distance that you will walk/climb from the stage to the end of walkway E. (A to E). Convert the final length to mm. Show all your calculations.

Note: The length of the stage is excluded.

Answer 1

AB = 5√(13) m ≈ 18.028 m (3 d.p.)

Total distance = 46,056 mm (nearest millimeter)

Explanation:

From observation of the given diagram, we can see that AB and CD are the hypotenuse of two right triangles. Therefore, to calculate the lengths of AB and CD, we can use Pythagoras Theorem.

`\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}`

For AB, the height of the right triangle is 10 m, and the base is the difference of 30 m and 15 m. Therefore:

• 
  `a = 10`
• 
  `b = 30 - 15 = 15`
• 
  `c = AB`

Substitute the values of a, b and c into the formula and solve for AB:

`\begin{aligned}10^2+15^2&=AB^2\\100+225&=AB^2\\325&=AB^2\\AB^2&=325\\AB&=√(325)\\AB&=√(5^2) \cdot 13}\\AB&=√(5^2)√(13)\\AB&=5√(13)\; \sf m\end{aligned}`

For CD, the height of the right triangle is 10 m, and the base is the difference of 50 m and 35 m. Therefore:

• 
  `a = 10`
• 
  `b = 50 - 35 = 15`
• 
  `c = CD`

As the values of a and b are the same as those for the calculation of length AB, this means that CD = AB:

`CD = AB = 5√(13)\; \sf m`

To calculate the total distance, sum the distances from A to E:

`\begin{aligned}\textsf{Total distance}&=AB+BC+CD+DE\\&=5√(13)+(35-30)+5√(13)+(55-50)\\&=5√(13)+5+5√(13)+5\\&=10+10√(13)\\&\approx 46.05551275...\; \sf m\end{aligned}`

As there are 1000 millimeters in one meter, to convert meters to millimeters, multiply the number of meters by 1000:

`\begin{aligned}46.05551275...* 1000&=46055.51275...\; \sf mm\\&=46056\; \sf mm\;(nearest\;millimeter)\end{aligned}`

Therefore, the total distance walked/climbed from the stage to the end of the walkway is 46,056 mm, rounded to the nearest millimeter.