6 (i) Surveyor's Land Plot

Question

ScanSolve AI Tutor · Accepted Answer

Here's the solution for question 6 from Section B.

6 (i) Surveyor's Land Plot

a) Draw a sketch of the plot.

Draw a right-angled triangle ABC with the right angle at A.
Label side AB = 10 m and side AC = 26 m.
Mark point D on AB such that BD = 3 m.
This means AD = AB - BD = 10 m - 3 m = 7 m.
Draw a line segment from C to D.
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.
Use the Pythagorean theorem in the right-angled triangle ABC.
$BC^2 = AB^2 + AC^2$ $BC^2 = (10)^2 + (26)^2$ $BC^2 = 100 + 676$ $BC^2 = 776$
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.
Consider the right-angled triangle ADC.
We know AD = 7 m and AC = 26 m.
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.
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.
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?
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 $\boxed{\text{Green}}$ .

6 (i) Surveyor's Land Plot

Step-by-step solution

Draw a right-angled triangle ABC with the right angle at A.

Label side AB = 10 m and side AC = 26 m.

Mark point D on AB such that BD = 3 m.

Draw a line segment from C to D.

Label the angle $\angle ACD$ as $\theta$ .

Use the Pythagorean theorem in the right-angled triangle ABC.

Calculate BC.

Consider the right-angled triangle ADC.

Use the tangent function to find $\theta$ .

Read the number of bottles for each color from the bar chart.

Sum the number of bottles for all colors.

Identify the color with the highest number of bottles from the table.

Still stuck on this one?

More English Questions

6 (i) Surveyor's Land Plot

Step-by-step solution

Draw a right-angled triangle ABC with the right angle at A.

Label side AB = 10 m and side AC = 26 m.

Mark point D on AB such that BD = 3 m.

Draw a line segment from C to D.

Label the angle ∠ACD\angle ACD∠ACD as θ\thetaθ.

Use the Pythagorean theorem in the right-angled triangle ABC.

Calculate BC.

Consider the right-angled triangle ADC.

Use the tangent function to find θ\thetaθ.

Read the number of bottles for each color from the bar chart.

Sum the number of bottles for all colors.

Identify the color with the highest number of bottles from the table.

Still stuck on this one?

More English Questions

Label the angle $\angle ACD$ as $\theta$ .

Use the tangent function to find $\theta$ .