Can you use trigonometry on any triangle

Explanation: For Trigonometric functions to work you need a hypotenuse, which you can only get in right triangles. Daniel L. Not only. Explanation: Although most often trigonometric functions are used with right triangles there are some situations when they can be used for any type of triangle. Examples: If you have two sides given and an angle between them you can use the trigonometric functions the Law of Cosines to calculate the third side.

Related questions How do I determine the molecular shape of a molecule? Three formulas make up the Law of Cosines. At first glance, the formulas may appear complicated because they include many variables. However, once the pattern is understood, the Law of Cosines is easier to work with than most formulas at this mathematical level. Understanding how the Law of Cosines is derived will be helpful in using the formulas.

The derivation begins with the Generalized Pythagorean Theorem, which is an extension of the Pythagorean Theorem to non-right triangles. Generally, triangles exist anywhere in the plane, but for this explanation we will place the triangle as noted. Recalling the basic trigonometric identities , we know that. The formula derived is one of the three equations of the Law of Cosines. The other equations are found in a similar fashion.

Keep in mind that it is always helpful to sketch the triangle when solving for angles or sides. In a real-world scenario, try to draw a diagram of the situation. As more information emerges, the diagram may have to be altered.

Make those alterations to the diagram and, in the end, the problem will be easier to solve. The Law of Cosines states that the square of any side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the other two sides and the cosine of the included angle. To solve for a missing side measurement, the corresponding opposite angle measure is needed. When solving for an angle, the corresponding opposite side measure is needed. We can use another version of the Law of Cosines to solve for an angle.

Given two sides and the angle between them SAS , find the measures of the remaining side and angles of a triangle. Find the unknown side and angles of the triangle in Figure. First, make note of what is given: two sides and the angle between them. Each one of the three laws of cosines begins with the square of an unknown side opposite a known angle. Because we are solving for a length, we use only the positive square root. Notice that if we choose to apply the Law of Cosines , we arrive at a unique answer.

For this example, we have no angles. We can solve for any angle using the Law of Cosines. See Figure. Because the inverse cosine can return any angle between 0 and degrees, there will not be any ambiguous cases using this method. Just as the Law of Sines provided the appropriate equations to solve a number of applications, the Law of Cosines is applicable to situations in which the given data fits the cosine models. We may see these in the fields of navigation, surveying, astronomy, and geometry, just to name a few.

This is accomplished through a process called triangulation, which works by using the distances from two known points. Suppose there are two cell phone towers within range of a cell phone. The two towers are located feet apart along a straight highway, running east to west, and the cell phone is north of the highway. Based on the signal delay, it can be determined that the signal is feet from the first tower and feet from the second tower.

Determine the position of the cell phone north and east of the first tower, and determine how far it is from the highway. For simplicity, we start by drawing a diagram similar to Figure and labeling our given information. This forms two right triangles, although we only need the right triangle that includes the first tower for this problem.

The cell phone is approximately feet east and feet north of the first tower, and feet from the highway. Calculating Distance Traveled Using a SAS Triangle Returning to our problem at the beginning of this section, suppose a boat leaves port, travels 10 miles, turns 20 degrees, and travels another 8 miles.

The diagram is repeated here in Figure. The boat is about Therefore we use the Sine Rule. The question involves angles. Therefore we use trig ratios - sin, cos and tan. The question does not involve angles. Therefore we use Pythagoras's Theorem. We do not know a side and its opposite angle. Therefore we use the Cosine Rule. Find the unknown side or angle in each of the following diagrams: a. Section 4: Sine And Cosine Rule Introduction This section will cover how to: Use the Sine Rule to find unknown sides and angles Use the Cosine Rule to find unknown sides and angles Combine trigonometry skills to solve problems Each topic is introduced with a theory section including examples and then some practice questions.

At the end of the page there is an exercise where you can test your understanding of all the topics covered in this page. You are allowed to use calculators in this topic. All answers should be given to 3 significant figures unless otherwise stated. Formulae You Should Know You should already know each of the following formulae: formulae for right-angled triangles formulae for all triangles NOTE: The only formula above which is in the A Level Maths formula book is the one highlighted in yellow.

You must learn these formulae, and then try to complete this page without referring to the table above. Then, input the numbers into the formula you have chosen.

How is trigonometry used on non-right angled triangles? Next, label the sides opposite each angle with its respective lowercase letter a Then simply input the values you have into the correct places of the formula. Answered by Bobbie C.