# S.L. Loney Solution of Triangles Solutions (Chapter 13)

SL Loney Plane Trigonometry Solutions for Chapter 13 ‘Solutions of Triangles’ discusses the basic concepts of solutions related to triangles for JEE and NEET. This chapter has many solved problems, theorems, and examples based on solutions of triangles. The SL Loney solutions of triangles chapter introduce you with the concepts of relations between sides and angles, sine and cosine rules for triangles, the half-angle formula for a triangle, semi-perimeter of a triangle, and area of a triangle.

SL Loney Plane Trigonometry Solutions of Triangles chapter plays an important role in the maths syllabus for JEE. It has 64 problems in total in 2 exercises. SL Loney Trigonometry detailed solutions is a resourceful book that will help you practice these problems thoroughly. You will be able to find the values of angles in a triangle when trigonometric ratios are given to you. In some cases, you would be given the sides of the triangles and you have to solve the triangles based on trigonometric ratios.

SL Loney Plane Trigonometry Solutions for Solutions of Triangles is an essential source to practice maths problems. Solving trigonometric problems related to triangles can be quite tricky and complex as they can’t be solved by just applying formulas. SL Loney solutions created by our academics experts help in understanding the concepts and applying the correct formula with utmost clarity. Our solutions help you develop the analytical skills to solve problems efficiently.

## Important topics for SL Loney Plane Trigonometry Solutions Chapter 13: Solutions of Triangles

This section includes a brief introduction of a few of the important topics covered in the chapter, solutions of triangles.

**Solutions of Triangles: **A triangle has three sides and three angles. Out of six elements, if three elements are given we could find the other three elements. The definition of solutions of triangles is, it is the process of calculating the sides of the angles of a triangle using given information. The solutions of triangles have two sections: first is the right angle triangle, and the second is acute or obtuse angle triangle.

**Right Angle Triangle:** A triangle that has its one angle equal to 90º is called a right-angle triangle. This section is further divided into four categories which help in solving the problems.

- The hypotenuse and one side are given to solve the problem.
- Two sides (hypotenuse side excluded) are given to solve the problem.
- One angle and one side (hypotenuse side excluded) are given to solve the problem.
- One angle and hypotenuse side are given to solve the problem.

**Acute/ Obtuse Angle Triangle: **This section is further divided into five categories which help in solving the problems. Those five-category are below-mentioned:

- All three sides of a triangle are given: Since all the three sides of a triangle are given, we can find the semi-perimeter (s) of a triangle, and derive the half-angle formulas using it. To find the angle we can use sine and cosine formulas of semi angles. The Sum of all the angles of the triangle is equal to 180º, so we need to find only two angles and the third one is found by simply subtracting the other two angles from 180º.
- Two sides and the included angle are given to solve the problem.
- Two sides and an angle opposite to one of the sides are given: Lets us consider side b and side c are two sides with opposite angle sin B is given to us then there are 3 cases possible to solve the problem:

- If b < c sin B, no such triangle is possible.
- If b = c sin B, it further has two cases:

**B is an obtuse angle:**cos B is negative, no such triangle exists.**B is an acute angle:**cos B is positive, one triangle exists.

- If b > c sin B, it further has the following cases:

**B is an acute angle:**cos B is positive, two triangles exist.**B is an obtuse angle:**cos B is negative, there are two possibilities here that is, either one triangle is possible or no triangle is possible. This is called an ambiguous case.- One side and two angles are given: The third angle is obtained by applying the sum of the triangle is equal to 180º theorem. The ratios of sides can be determined using proper formulas.
- Three angles of the triangle are given: We are unable to find the magnitude of the sides; only the ratio of the sides can be found using the formulas.

### Exercise Discussion for SL Loney Plane Trigonometry Solutions Chapter 13: Solutions of Triangles

Solutions of Triangles of SL Loney Plane Trigonometry has 64 solved problems divided into two exercises:

- In exercise 1, there are 4 questions along with a few examples on the topic of the right-angle triangle. The questions asked are generally based on finding the sides of a right-angled triangle if aside and an angle is given, solving the triangle if two sides and the angle included are given, finding the angles if the length of perpendicular and all the sides are given and finding the acute angle whose hypotenuse is given.
- In exercise 2, there are 60 problems along with a few examples on the topic of not right-angle triangles. The questions asked are generally based on finding the degree of smallest angle, the degree of greatest angle, solving the triangle, finding the greatest angle using logarithmic, the sides, the ratio of the sides, and finding whether the triangle is ambiguous or not.

## Why Use SL Loney Plane Trigonometry Solutions Chapter 13: Solutions of Triangles by Instasolv?

- SL Loney Plane Trigonometry Solutions for Solutions of Triangles by Instasolv solution help you develop a deeper understanding of complex mathematical concepts and improve your skills to solve problems.
- SL Loney Solutions are designed by academic experts who can articulate the concept in the most efficient way.
- Our SL Loney Solutions are 100% accurate and are based on the latest JEE syllabus.
- These solutions help in flourishing math fluency and solving the complex problem efficiently.