6 (i) Surveyor's Land Plot
This English question involves literary analysis, grammar, or writing skills. The detailed response below provides a well-structured answer with supporting evidence and clear explanations.
ScanSolve AI Answer
Here's the solution for question 6 from Section B.
6 (i) Surveyor's Land Plot
a) Draw a sketch of the plot.
Step 1: Draw a right-angled triangle ABC with the right angle at A.
Step 2: Label side AB = 10 m and side AC = 26 m.
Step 3: Mark point D on AB such that BD = 3 m. This means AD = AB - BD = 10 m - 3 m = 7 m.
Step 4: Draw a line segment from C to D.
Step 5: Label the angle $\angle ACD$ as $\theta$.
The sketch would look like this:
`
C
| \
| \
26m| \
| \
| \
A-----D-----B
|--7m--|--3m--|
10m
`
b) Help him to get the length of the side BC.
Step 1: Use the Pythagorean theorem in the right-angled triangle ABC.
$$ BC^2 = AB^2 + AC^2 $$
$$ BC^2 = (10)^2 + (26)^2 $$
$$ BC^2 = 100 + 676 $$
$$ BC^2 = 776 $$
Step 2: Calculate BC.
$$ BC = \sqrt{776} $$
$$ BC \approx 27.85678 $$
The length of the side BC is $\boxed{27.86 \text{ m}}$ (rounded to two decimal places).
c) Calculate the value of $\theta$ to two decimal places.
Step 1: Consider the right-angled triangle ADC.
We know AD = 7 m and AC = 26 m.
Step 2: Use the tangent function to find $\theta$.
$$ \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{AD}{AC} $$
$$ \tan(\theta) = \frac{7}{26} $$
$$ \theta = \arctan\left(\frac{7}{26}\right) $$
$$ \theta \approx \arctan(0.2692307) $$
$$ \theta \approx 15.076^\circ $$
The value of $\theta$ is $\boxed{15.08^\circ}$ (rounded to two decimal places).
6 (ii) Coloring Materials Bar Chart
a) Using the bar chart, copy and complete the following table.
Step 1: Read the number of bottles for each color from the bar chart.
• Red: 25 bottles
• Blue: 15 bottles
• Green: 28 bottles
• Yellow: 20 bottles
• Black: 10 bottles
• White: 12 bottles
| Color | Red | Blue | Green | Yellow | Black | White |
| :-------------- | :-- | :--- | :---- | :----- | :---- | :---- |
| Number of bottles | 25 | 15 | 28 | 20 | 10 | 12 |
b) Find the total number of bottles of coloring materials in the workshop.
Step 1: Sum the number of bottles for all colors.
$$ \text{Total bottles} = 25 + 15 + 28 + 20 + 10 + 12 $$
$$ \text{Total bottles} = 110 $$
The total number of bottles is $\boxed{110}$.
c) What is the modal color?
Step 1: Identify the color with the highest number of bottles from the table.
Green has 28 bottles, which is the highest frequency.
The modal color is $\boxed{\text{Green}}$.
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