MATHEMATICS NOTES FORM 2 TOPIC 9: TRIGONOMETRY
UNAWEZA JIPATIA NOTES ZETU KWA KUCHANGIA KIASI KIDOGO KABISA:PIGA SIMU:0787237719
Do you want to learn the relationships involving lengths and Angles of right-angled triangle? Here, is where you can learn.
Angles of Elevation and Angles of Depression
Demonstrate angles of elevation and angles of depression
Angle of Elevation of an Object as seen by an Observer is the angle between the horizontal and the line from the Object to the Observer’s aye (the line of sight). See the figure below for better understanding
The angle of Elevation of the Object from the Observer is α0.
Angle of depression of an Object which is below the level of Observer is the angle between the horizontal and the Observer’s line of sight. To have the angle of depression, an Object must be below the Observer’s level. Consider an illustration below:
The angle of depression of the Object from the Object is β0
Problems involving Angles of Elevation and Angles of Depression
Solve Problems involving angles of elevation and angles of depression
From the top of a vertical cliff 40 m high, the angle of a depression of an object that is level with the base of the cliff is350. How far is the Object from the base of the cliff?
We can represent the given information in diagram as here below:
Angle of depression = 350
1. Use trigonometric tables to find the following:
- cos 38.250
- sin 56.50
- tan 750
2. Use trigonometrical tables to find the value of x in the following problems.
- sin x0 = 0.9107
- tan x0 = 0.4621
3. Find the height of the tower if it casts a shadow of 30 m long when the angle of elevation of the sun is380.
4. The Angle of elevation of the top of a tree of one point from east of it and 56 m away from its base is250. From another point on west of the tree the Angle of elevation of the top is500. Find the distance of the latter point from the base of the tree.
5. A ladder of a length 15m leans against a wall and make an angle of300with a wall. How far up the wall does it reach?