Determining the Angle of Elevation Using Tangent

Pupils work in pairs to investigate what it takes to prove that two triangles are similar. They work through various shortcuts to find which are enough to show a similarity relationship between the triangles. Small groups work with the...

Is this enough to show the two triangles are congruent? Small groups work through different combinations of constructing triangles from congruent parts to determine which combinations create only congruent triangles. Participants use the...

Introduce your classes to a new world of mathematics. Pupils learn to call trigonometric ratios by their given names: sine, cosine, and tangent. They find ratios and use known ratios to discover missing sides of similar triangles. 

Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of the...

Right triangles are so special! Use special right triangles to discover the trigonometric ratios. Pairs construct special right triangles and find the values of the ratios of the sides. In the process, they discover the ratios stay the...

What does geometry have to do with depression? It's an angle of course! Learners apply the tangent ratio to problem solving questions by finding missing lengths. Problems include angles of elevation and angles of depression. Pupils make...

Interpret and apply the relationships between tangent and secant lines. The instructor explains the relationships of the angles and segments created by intersecting tangent and secant lines. 

Half of an equilateral triangle is a special right triangle. A video instructor shows how to find the pattern of the side lengths for a 30-60-90 triangle. She then applies the relationship to different examples.

45-45-90 triangles are half a square, which gives them a special status! The instructor explains the relationship of the sides of the 45-45-90 triangle using the Pythagorean Theorem as a reference. 

What makes an equilateral triangle equilateral? It turns out it's much more than just the side lengths! Learners analyze four different triangles to determine the best equilateral triangle. They create a formula that they later use to...