Use knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem Apply concepts of bearings and right triangle trigonometry to topographic maps
Conceptual Framework
perspective measurement, space, representation in the context of orientation in space and time
Statements of Inquiry
Understanding perspective enables us to represent and locate one's position in space, on earth, or on a two dimensional representation of our surroundings
Factual
How do we calculate bearings and reverse bearings?
Conceptual
What is the link between an angle measure and the ratio of side lengths in right triangles?
Debatable
Has technology eliminated the need to perform manual calculations when navigating or map reading?
Description
This course will enable students to begin to develop a spatial awareness as they investigate relationships in two and three dimensions. Students are introduced to the concepts of similarity and use similar triangles to solve problems. The unit progresses naturally into solving for missing sides and angles in right-angled triangles using trigonometry. Relevant real-life applications are explored as students learn how to measure bearings with a compass , calculate angles of elevation and depression in the context of navigation, surveying and cartography. The unit culminates with an interesting task of locating a downed pilot in the Canadian Rockies, whereby students learn to read contour maps, determine search areas and devise plans for his rescue.
Learning Outcomes
Label the parts of a right angled triangle
Construct a right angled triangle in Geogebra
Use the Pythagorean theorem to find a missing side in a right angled triangle
Prove that two triangles are similar
Use the concept of similar triangles to find missing values
Apply similar triangles to solve problems in a real world context
Investigate and consolidate understanding of the three primary trigonometric ratios – sine, cosine and tangent
Find the sine, cosine and tangent for an angle of a right triangle – exact or approximate values using a GDC
Use SOHCAHTOA to find missing sides and angles in right angled triangles
Find the exact values of sine, cosine and tangent for 30, 45, 60 using special triangles
Solve problems involving right angled triangles using SOHCAHTOA
Use right triangle trigonometry to calculate angles of elevation and distances
Find the bearing of a point A from a point B
Construct scale diagrams given lengths and bearings
Solve problems involving bearings
Apply bearings to a real life situations including navigation and topographic maps