MM3 – Similarity of two-dimensional Figures, Right-Angled Triangles

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Objective - To use basic trigonometry to solve right triangles.

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Presentation transcript:

MM3 – Similarity of two-dimensional Figures, Right-Angled Triangles Vocabulary (as per MM1 and MM2): accuracy adjacent angle of depression angle of elevation area capacity composite figure cosine ratio cylinder error field diagram hypotenuse opposite perimeter quadrant rate ratio right prism scale diagram scale factor scientific notation significant figures similar sine ratio standard prefix tangent ratio trigonometry unitary method volume

Basic Concepts: Calculate measurements from scale diagrams Calculate and use scale factors for similar figures Calculate sine, cosine and tangent ratios and use them to find side lengths and angles in triangles Calculate angles of depression and elevation Solve practical problems using scale factor and trigonometry

Similar Figures Two figures are similar if one is an enlargement of the other. An enlargement factor is the same as the scale factor.

Scale Drawings A scale drawing is a representation of the original, with all angles the same and all sides in proportion to the original.

NOTE: The majority of activities in this section depend on measurement – see textbook for more questions.

Right-Angled Trigonometry You SHOULD remember working with Pythagoras’ Theorem and trigonometry from junior school…

Pythagoras

The three trigonometric ratios: These three ratios can be used to find sides or angle in triangles: A good visual cue for this is: 𝑺 𝑶 𝑯 𝑪 𝑨 𝑯 𝑻 𝑶 𝑨

Using your calculator

More Calculator Work…

Finding angles using trigonometry

Finding sides in triangles using trigonometry:

Unknown in the Denominator

Angles of Elevation and Depression The angle of elevation Is when you look UP at an object. The angle of depression is when you look DOWN at an object. Both are measured from the horizontal.

Applications to problems