Which problem types can be used to solve a triangle using the law of sines?
Table of Contents
- 1 Which problem types can be used to solve a triangle using the law of sines?
- 2 How many triangles can be formed with AAS?
- 3 How many solutions does a triangle with side lengths?
- 4 How do you find the other two sides of a triangle?
- 5 What are the different types of triangles?
- 6 How many sides does an isosceles triangle have?
Which problem types can be used to solve a triangle using the law of sines?
It is valid for all types of triangles: right, acute or obtuse triangles. The Law of Sines can be used to compute the remaining sides of a triangle when two angles and a side are known (AAS or ASA) or when we are given two sides and a non-enclosed angle (SSA). We can use the Law of Sines when solving triangles.
How many triangles can be formed with AAS?
Given triangular parts SSS, ASA or AAS always guarantees a single, unique triangle. Given the triangular parts SSA, however, is different and leaves the triangle unclear, or ambiguous. The “Ambiguous Case” (SSA) occurs when we are given two sides and the angle opposite one of these given sides.
How many possible triangles can be formed?
Since there is exactly one triangle, there is one solution. Case 3 is referred to as the Ambiguous Case because there are two possible triangles and two possible solutions….SSA Triangles.
| If: | Then: | |
|---|---|---|
| c. | \begin{align*}a > b\end{align*} | One solution |
How many solutions does a triangle with side lengths?
As you now know, when two sides of a triangle with an included side are known, and the lengths of the two sides are equal, there is one possible solution. Since an isosceles triangle meets these criteria, there is only one possible solution.
How do you find the other two sides of a triangle?
If we are given an angle and a side length, then we can use trigonometry ratios to find the other two sides. As per the sine, cosine and tangent ratios, in a triangle, if θ is the angle between two sides, then; Sine θ = Length of opposite side/Length of Hypotenuse side Cos θ = Length of Base side/Length of Hypotenuse side
What is the formula to find the right triangle side lengths?
b = √ (c² – a²) for hypotenuse c missing, the formula is. c = √ (a² + b²) Given angle and hypotenuse. Apply the law of sines or trigonometry to find the right triangle side lengths: a = c * sin (α) or a = c * cos (β) b = c * sin (β) or b = c * cos (α) Given angle and one leg.
What are the different types of triangles?
Also, we will come across different types of triangles based on the length of the sides. Basically, there are three types, based on sides of the triangle, which are: Scalene Triangle: The triangle where all sides are unequal. Isosceles Triangle: The triangle where only two sides are equal, and the angles opposite the equal sides are also equal.
How many sides does an isosceles triangle have?
An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side? The triangles ABC and A “B” C “are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A “B” C “.