Here is a bundle of recommended readings before getting started with this lesson.
Try your knowledge on these topics.
Consider the triangle with vertices A, B, and C.
On a June night, Zosia observes an astronomical asterism, which is called the Summer Triangle.
The applet below shows two different cases for a triangle with vertices A, B, and C. Case I shows the lengths of two sides and the measure of their included angle. Case II shows the lengths of all three sides.
Consider △ABC with sides of length a, b, and c, which are respectively opposite the angles with measures A, B, and C.
The following equations hold true with regard to △ABC.
Kriz wants to determine the distance between two trees on the other side of the river. Kriz uses a tool that measures the distances to objects. The tool is able to find the distances to each tree as 4 meters and 3.5 meters.
The angle between these sides, from where the Kriz stands with the measuring tool, measures Find the distance between the trees, and round the answer to the nearest tenth of a meter.
For simplicity, the vertices and sides of the triangle will be named.
As the diagram indicates, the light rays form a triangle. In this triangle, the three side lengths are known.
The measure of the three angles will be found one at a time.
In △ABC, all three side lengths and the measure of the angle at C are given. Examine how the length of AB changes as the measure of ∠C varies.
|m∠C||Relationship between a2+b2 and c2||Conclusion|
|c2<a2+b2||If ∠C is acute, not too many conclusions can be made. The opposite side to ∠C can be the largest side, the shortest side, or none.|
|c2=a2+b2||The cosine of is 0. In this case, the Law of Cosines becomes the Pythagorean Theorem. This means that the opposite side to ∠C is the largest side of the triangle.|
|c2>a2+b2||If ∠C is obtuse, its measure is greater than the measures of ∠A and ∠C. Therefore, its opposite side is the largest side of the triangle.|
First, SD and DN will be found. Then, the Law of Cosines will be used to find NS, the distance between New York and San Juan.
Approximate to nearest hundred