Angles of Elevation and Depression (10)

Solve right-angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245)

LO: To solve right-angled triangle problems using angles of elevation and depression.

Know:

  • the properties of right-angled triangles.

  • the trigonometric ratios and how to use them in context.

Understand:

  • That we can use angles of elevation and depression to solve right-angled triangle problems.

Do:

  • I can solve right-angled triangle problems involving angles of elevation and depression.

Properties of Right-Angled Triangles

“Opposite” is the opposite to the angle.
“Adjacent” is next to to the angle.
“Hypotenuse” is the long side of the right-angled triangle.

Trigonometric Ratios

There are 3 ratios to help identify the length of the sides.

sin angle = opposite side / hypotenuse

cos angle = adjacent side / hypotenuse

tan angle = opposite side / adjacent side

BBC Trigonometry

Angles of Elevation and Depression

“Angle of depression and angle of elevation of 2 objects are identical.”

Angles of elevation and depression is fairly easy to calculate once you understand their position.

Elevation means to “move up“, think of an elevator to help you go up many flights of stairs.

Depression means to “move down“, think of being depressed. It means to be down on yourself.

If you can remember back to the angles unit when we talked about angles in parallel lines, angles of depression and elevation create “alternate angles”. Which means that they are equivalent or equal.

One common misconception in terms of angles of depression is that the angle of depression is always compared to the horizon and not compared to the vertical object.

Bearings and Direction

Bearings can be used to indicate directionality. There are two types of bearings, True bearings and Compass Bearings.

True bearings are measured from north in a clockwise direction and are represented using three digits.

Compass bearings are measured from north (N) or south (S), and include the angle from the starting point followed by the direction east (E) or west (W).

Trigonometry can also be used to find the distance of 2 objects based on bearings and direction.

Interactives

Angles of Elevation and Depression Videos

Bearings Videos

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