CK-12 Foundation
Alternate Formula for the Area of a Triangle: Alternate Area of a Triangle
It's always nice to have a plan B. Pupils investigate an alternate formula for the area of a triangle that uses sine. A set of challenge questions shows how the new formula relates to the well-known formula of (1/2)bh.
EngageNY
An Area Formula for Triangles
Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....
EngageNY
Using Trigonometry to Determine Area
What do you do when you don't think you have enough information? You look for another way to do the problem! Pupils combine what they know about finding the area of a triangle and trigonometry to determine triangle area when they don't...
Alabama Learning Exchange
Triangle Area: No Height? Use the Sine
No height? No problem! Learners use their knowledge and a little help from GeoGebra to develop the Law of Sines formula. The Law of Sines helps to determine the height of triangles to calculate the area.
CK-12 Foundation
Determination of Unknown Triangle Measures Given Area: Jib Sheets
Solving triangles is a breeze. Young boat enthusiasts solve problems involving triangles in the context of sails on a boat. They must apply different strategies, including the Law of Cosines and area formulas.
Curated OER
Area of Triangle Using Trigonometry
In this trigonometry worksheet, learners determine the area of triangles using the trigonometry ratios of sine, cosine, and tangent. This one-page worksheet contains ten problems.
Mathed Up!
Sine and Cosine Rules and Area of Triangles
Learners discover how to find missing sides and angles using trigonometry. Scholars first watch a video covering the Law of Sines and Cosines, as well as the area formula for a triangle. To test their knowledge, they complete a learning...
Mathematics Vision Project
Module 5: Modeling with Geometry
Solids come in many shapes and sizes. Using geometry, scholars create two-dimensional cross-sections of various three-dimensional objects. They develop the lesson further by finding the volume of solids. The module then shifts to finding...
Curated OER
A Special Relationship
Students discover the relationships of the lengths of the sides of right triangles and right triangles using a series of drawings on dot paper. They investigate and solve problems of standard (customary and metric units) and non-standard...
Alabama Learning Exchange
"I Saw the Sine"
Discover trigonometric ratios that complement each other. Using two videos, the lesson introduces the trigonometric ratios. The class discovers the relationship between the sine and cosine of complementary angles.
Curated OER
Area of a Triangle
Students solve the area of triangles. For this precalculus lesson, students are given two sides of a triangle and asked to calculate the area. They apply the law of sine and the side-angle-side area formula to solve.
Curated OER
The Law of Sines
In this law of sines activity, students use the law of sines to find the missing measurement in a triangle. They determine the value of angles and the lengths of triangles. Students compute the area of triangles. This four-page activity...
Curated OER
Law of Sines and Cosines
In this sine and cosine worksheet, students solve given triangles using the law of sines and cosines. They determine the area of triangles. This three-page worksheet contains 12 multi-step problems.
Chapman University
A Pythagorean-Style Proof of the Sine Sum-of-Angles Formula
This well organized poster shows a step-by-step algebraic proof and related graphic. Understanding how formulas were derived, connects learners to the idea that the study of mathematics is continuous and cumulative. Learners will also...
National Council of Teachers of Mathematics
Improving Archimedes' Method
For this Archmides' method instructional activity, high schoolers determine the area of a regular n-gon inscribed in a circle. They use sine and cosine functions to solve problems. This three-page instructional activity contains 4...
Mathematics Vision Project
Module 7: Modeling with Geometry
Model good modeling practices. Young mathematicians first learn about cross sections and solids of revolution. They then turn their attention to special right triangles and to the Laws of Sine and Cosine.
Curated OER
Law of Sines and Cosines
Students solve problems using sine and cosine. In this precalculus lesson, students apply the properties of sine and cosine to solve non-right triangle problems. They use Heron's Law to find the area of a shape.
Curated OER
Sine and Cosine
Students solve problems using sine and cosine. In this precalculus lesson, students solve word problems using sine and cosine. They identify where it is appropriate to laws of sine and cosine and where to use the Pythagorean Theorem.
Curated OER
Law of Sines and Law of Cosines
In this Pre-calculus/Trigonometry worksheet, students use the laws of sines and cosines to solve triangles. The four page worksheet contains thirteen problems. Answers are not included.
Curated OER
Trigonometry Worksheet
For this trigonometry worksheet, students use the law of sines to find the length of a missing side of a triangle. They prove trigonometric identity and use Heron's formula to find the area of a triangle. This two-page worksheet...
Curated OER
The Law of Sines
Learners define the laws of sine as it relates to a right triangle. In this trigonometry lesson, students identify the properties of sine to help then find mixing sides of a right triangle. They also solve for the missing angles.
Curated OER
Trigonometric Triangles
In this trigonometry learning exercise, students find the missing angle and sides given the 6 trigonometric values. There are 6 questions with an answer key.
Curated OER
Section 6.1-6.2 Precalculus: Trigonometry
In this trigonometry instructional activity, students solve 15 triangle problems. Students use the law of sines and law of cosines to find the missing angles and side lengths of a triangles.
Curated OER
Law of Sine and Cosine
Students solve problems using the law of sine and cosine. In this precaclulus lesson, students learn the law of DeMoivre's Theorem and Heron's theorem. They use both theorems to solve problems.