**SUBJECT: MATHEMATICS**

**CLASS: JSS 3**

**DATE:**

**TERM: 2nd TERM**

WEEK EIGHT** **** **** **** **** **** Date:…………………….**

**TOPIC: ANGLES OF ELEVATION AND DEPRESSION**

**CONTENT:** i) Horizontal and vertical lines

**ii) Angles of elevation**

** iii) Measuring angles of elevation and depression.**

** **

**Horizontal and Vertical Lines**

**Horizontal lines are lines that are parallel to the surface of the earth. For example, the surface of a liquid in a container, floor of a classroom, etc. See the diagram below:**

** Horizontal line**

**Vertical lines are lines that are perpendicular to the horizontal surface, e.g. wall of a classroom, a swing pendulum, etc.**

** **

** **

** Vertical line **

** **

** **

**Evaluation:**

** Say whether the following are horizontal or vertical or neither.**

**a) A table top b) A door c) A table leg d) Top edge of a wall.**

** **

**READING ASSIGNMENT**

**NGM Bk 2 Chapter 20, Page 165**

**Essential Mathematics for JSS Bk 2, Chapter 17, Pg 173**

** **

**Angles of Elevation**

**The angle of elevation of an object for a given point above the surface of the earth is the angle formed between the horizontal plane and the view point of the object. See the diagram below. T**

** T**

** **

** **

** V F **

** VF Horizontal plane**

** V = View point, T = Top where the object is, F = Foot of the vertical plane **

** e = angle of elevation**

** **

**Reference:**

**NGM Bk 2 Chapter 20, Page 165**

**Essential Mathematics for JSS Bk 2, Chapter 17, Pg 173**

** **

**Angle of Depression**

**The angle of depression of an object from a given point T is angle from the horizontal line above the earth’s surface and the vertical surface.**

** Horizontal T**

** h**

** Thus, the angle of elevation is equal in size to the angle of depression. (alternate angles are equal i.e. d = e)**

** **

**Measuring Angles of Elevation and Depression**

**When constructing angles of elevation and depression, the use of scale drawings is necessary in order to have effective construction of angles**

** **

**Worked Examples**

**Consider the diagram below; find the height of the flagpole to the nearest metre using suitable**

** scale.**

** F**

**Q 10m T**

**Solution**

** By construction, choose a scale of 1cm represent 2m.**

** The height of the flagpole PT = 3cm, converted to m, will give 2 × 3 = 6.**

**Example 2: The angle of elevation of the top of a tower to a point 42m away from its base on **

** level ground is 360, find the height of the tower.**

**Solution **

** T**

** 3 R**

** 42m**

** By construction, using a suitable scale of 1cm represented by 6m, then PR = 42/6 = 7cm.**

** The length TR = 5.0cm. Converting back to metre, we have;**

** Length TR = 5 × 6 = 30m**

**Example 3: From the top of a bulding 20m high, the angle of depression of a car is 450, find the distance of the car from the foot of the building.**

**Solution**

**Rough sketch: T**

** C 20m F **

**T = Top of the building, C = Car, F = Foot of the building**

**CF is the distance of the car from the foot of the building. **

**Since angle of depression equals angle of elevation;**

**By construction, using a suitable scale of 1cm represents 5m**

**For 20m, we have 20/5 = 4cm**

**Length CF = 4cm**

**By conversion, length CF = 4 × 5 = 20m.**

** **

**Evaluation: **

**A tower PQ is 10m high, if the distance from point R to P is 50m on the ground, find the**

**angle of elevation of Q from R.**

** **

** Q**

** **

** 10m**

** **

** **

** P 50m R**

**From the top of a cliff of 200m high, Dele observes that the angle of depression of a boat at**

** sea is 350, find the distance between the boat and the foot of the cliff.**

** **

**READING ASSIGNMENT**

**NGM Bk 2 Chapter 20, Page 166 - 169**

**Essential Mathematics for JSS Bk 2, Chapter 17, Pg 176 – 177.**

** **

**WEEKEND ASSIGNMENT**

**Objective**

**Calculate the size of the fourth angle if three angles of a quadrilateral are 650, 1150, and 1250 respectively. a) 350 b) 550 c) 450 d) 750****Calculate the number of sides of a regular polygon whose total angle is 10800. a) 4 b) 6 c) 8 d) 10****PQRS is a rectangle with sides 3cm and 4cm, if its diagonal cross at O, calculate the length of PO. a) 3.5cm b) 5.0cm c) 2.5cm d) 4.0cm****If the angles of a pentagon could be x, 2x, 4x and 5x respectively, what would be the value of x? a) 600 b) 900 c) 150 d) 300**

** **

**THEORY**

**From the top of a building 50m high, the angle of depression of a car is 550, find the distance of the car from the foot of the building.****Find the height of the flagpole in the diagram below to the nearest metre.**

** F**

** **

** **

** 20cm**

** **

**B C**

** 8cm **

** **

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