OBJECTIVE - G.SRT.D.9

Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

INTERPRETATION OF OBJECTIVE - G.SRT.D.9

This is a nice use for the trigonometric ratios. We can easily express the height of a triangle in terms of sine. This also nicely leads us into the next objective about deriving the law of sines.

SKILLS

(1) The student will be able to derive the area formula for a triangle using the sine ratio.

(2) The student will be able to determine the area of a triangle given a variety of information.

THE BIG IDEA

Information about a triangle doesn't usually include its height. Using trigonometry we are able to provide students with a way to solve for the area of a triangle using angles and sides. The Big Idea is that trigonometry helps us solve lots of different problems and area is one of them.

TRAPS & PITFALLS

No traps or pitfalls that I know of.

PAST CONNECTIONS

We of course connect to the trigonometric ratios that we just learned. It is the sine ratio that allows us to determine the height of the triangle.

FUTURE CONNECTIONS

Students will use the concept of dropping an alitude to a side and forming two right triangles within any triangle to derive the law of sines and the law of cosines.

MY REFLECTIONS (over line l)

This is quite an easy concept and yet it leads nicely into the Law of Sines and Cosines relationships. This is a nice preparatory relationship to derive because it gives students an idea of how we can use right triangle trigonometry to solve things in oblique triangles.