Question

1. A MAP SCALE READS 1CM:5KM. IF A DISTANCE ON THE MAP MEASURES 7CM, THE ACTUAL DISTANCE WILL BE?. 2. A SCHOOL DINING HALL IS 35M LONG. IF ON A PLAN, THIS LENGTH IS REPRESENTED BY 7CM, WHAT IS THE SCALE?. 3. THE LENGTH OF A BUILDING IS 30 METRES. A SCALE DIAGRAM OF THE BUILDING IS BEING DRAWN TO A SCALE OF 1CM TO 5 METRES. THE LENGTH OF THE BUILDING ON THE SCALE DIAGRAM IS?. 4. IF THE ANGLE OF ELEVATION OF A FROM B IS 42°, WHAT IS THE ANGLE OF DEPRESSION OF B FROM A?. 5. A BOY IS FLYING A KITE, THE STRING IS 25M LONG AND IS AT AN ANGLE OF 42° WITH THE HORIZONTAL, USING A SCALE DIAGRAM, FIND HOW HIGH THE KITE IS ABOVE THE BOY’S HEAD?

Answer 1

1. 35 km

2. 1 cm to 5m

3. 6 cm

4.
`42^\circ`

5. 16.73 m

Explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map = 7 cm

Actual distance = Measurement of map
`* 5`

Actual distance = 7
`* 5` = 35 km

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Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

-------------------

Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to
`(1)/(5)` cm on scale

30m is equivalent to
`(1)/(5) * 30` = 6 cm on scale

-------------------

Solution 4.

Angle of elevation of A from B =
`42^\circ`

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A =
`42^\circ`

-------------------

Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal,
`\angle B = 42^\circ`

Please refer to the attached image for the clear understanding of the situation.

To find:

Height, AC = ?

We can use trigonometric identity:

`sin\theta = (Perpendicular)/(Hypotenuse)`

OR

`sinB = (AC)/(BC)\\\Rightarrow sin42^\circ = (AC)/(25)\\\Rightarrow AC = 25 * 0.67\\\Rightarrow AC = 16.73 m`

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So, the answers are:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4.
`42^\circ`

5. 16.73 m