**SUBJECT: MATHEMATICS**

**CLASS: JSS 2**

**DATE:**

**TERM: 3rd TERM**

**REFERENCE**

- WABP ESSENTIAL MATHEMATICS FOR JSS BK 2 BY A.J.S. OLUWASANMI
- NEW GENERAL MATHEMATICS BY J.B. CHANNON & ETAL

WEEK 3** **** **** **** **** **** **** **** ****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 earth. For example, the surface of a liquid in a container, floor of a classroom, etc. Seethe 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.**

**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 well**

** **

**Reading Assignment**

**NGM BK 2 Chapter 17, pg 173**

**Essential Mathematics for JSS BK 2, Chapter 17, pg 173**

** **

**Angles of Elevation **

**The angle of elevation of an object from a given point is the angle formed when an observer looks up to see an object his head. See the diagram below. **

** **

** **

** angle of **

**elevation**

** **

** **

** Horizontal plane**

**V = view point, T = top where the object is, F = foot of the vertical plane, e = angle of elevation**

** **

**Reading Assignment**

**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 the angle formed when an observer looks down to see an object below his head.**

** **

** Horizontal **

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

**NGM BK 2 Chapter 20, pgs 166 – 167**

**Measuring Angles of Elevation and Depression **

**When constructing angles of elevation and depression, the use of scale drawing is necessary in order to have effective construction of angle. Consider the diagram below; find the height of the flagpole to the nearest metre using suitable scale. **

**Solution **

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

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

**Example 2:** The angle of elevation of the top of a tower 42m away from a point on the level ground is 36o, find the height of the tower.

**Solution **

**By construction, using a suitable scale of 1cm represented by 6cm, then PR = 426= 7cm**

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

**Length TR = 5 x 6 = 30m**

**Example 3: **From the top of a building 20m high, the angle of depression of a car is 45o, find the distance of the car from the foot of the building.

**Solution **

**Rough sketch:**

**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 equal angle of elevation;**

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

**For 20m, we have 205 = 4cm**

**Length CF 4cm**

**By conversion, length CF = 4 x 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**

**From the top of a cliff of 200m high, Martins observes that the angle of depression of a boat at sea is 35o, find the distance between the boat and the foot of the cliff.**

**GENERAL EVALUATION**

**A boat is 180m from the foot of a vertical cliff of height 80m. find by scale drawing the angle of depression of the boat measured from the top of the cliff.****A boy is flying a kite. The string is 25m long and is at an angle of 42o with the horizontal. Using a scale diagram, find the high the kite is above the boy’s head?**

** **

**REVISION QUESTION**

**The angle of elevation of point P from point Q is 40o. PQ = 45km. How high is point P above the level of point Q.****A girl with eyes-level height of 1.65m observes that the angle of elevation of the top of the tower 20m away is 40o. Calculate the height of the tower.**

** **

**READING ASSIGNMENT**

**NGM BK 2 chapter 20, page 166 – 169**

**Essential mathematics for JSS BK 2, chapter 23, pg 295 – 297**

**Exercise 23.1 No 1, 2 & 3 page 296**

** **

**WEEKEND ASSIGNMENT**

**Calculate the size of the fourth angle if three angles of quadrilateral are 65o, 115o and 125o respectively A. 35o B. 55o C. 45o D. 75o****Calculate the number of side of a regular polygon whose total angles is 1080o A. 4 B. 6 C. 8 D. 10****PRQS is a rectangle with the side 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 angle of a quadrilateral could be x, 2x, 4x and 5x respectively, what would be value of x? A. 60o B. 90o C. 15o D. 30o****If the angle of elevation of a building from a point on the ground is 43o. What is the angle of depression? A. 47o C. 53o C. 43o D. 32o**

** **

**THEORY**

**From the top of a building 50m high, the angle of depression of a car is 55o, 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.**

**flagpole**

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