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Mathematics has various important branches such as algebra, geometry, probability, trigonometry, arithmetic, and lots more. We know that geometry is the study of different shapes, sizes, and positions of different shapes based on the number of sides, angles, and so on. Whereas trigonometry is the subset of geometry that deals with the properties of one of the shapes in geometry called “Triangle”. Both trigonometry and geometry seem to be related to each other, but of course, they are not the same. In this article, let us discuss the difference between geometry and trigonometry with some detailed explanation.

Trigonometry can be considered as a subset of geometry. In modern mathematics, trigonometry plays a huge role. Trigonometry is mostly about studying various properties of triangles, lengths, and angles. However, it also deals with waves and oscillations. In trigonometry, we mostly study the relationships between the side lengths and angles of a right-angle triangle. There are six trigonometric relations. Three basic ones, named Sine, Cosine, and Tangent, are clubbed together with Secant, Cosecant, and Cotangent. Let us consider that we have a right-angled triangle. The three sides will be height, base, and hypotenuse respectively. Then we can define the fundamental trigonometric relations as follows:

sin A=(height)/(hypotenuse)

cos A=(base)/(hypotenuse)

tan A=(height)/(base)

Cosec, Sec, and Cot can also be stated as the reciprocal of Sine, Cosine, and Tangent respectively. Trigonometry is not just a study about simple plane figures. It has a branch called spherical trigonometry, which studies triangles in three-dimensional spaces.

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Geometry is defined as the study of various sizes, shapes, and properties of vacant spaces of a given number of dimensions such as 2D or 3D. Euclid, the great mathematician, had made a huge contribution to the domain of geometry. Therefore, he is known as the Father of Geometry. Geometry can be categorized into the following -

Plane geometry,

Solid geometry, and

Spherical geometry.

Plane geometry deals with two-dimensional geometric objects such as points, lines, curves, and various plane figures such as circles, triangles, and polygons. Solid geometry studies three-dimensional objects such as various polyhedra, spheres, cubes, prisms, pyramids, and so on. Spherical geometry also studies three-dimensional objects such as spherical triangles and spherical polygons. Geometry can also be categorized into Euclidean Geometry, the study of flat surfaces, and Riemannian geometry. in which the fundamental subject is the study of curved surfaces.

This is the difference between trigonometry and geometry. This describes what’s the difference between trigonometry and geometry.

**1. **Consider ABCD is a parallelogram such that AB is parallel to DC and DA is parallel to CB. The side AB is of length 20 cm. E is a point between A and B such that AE is 3 cm. F is a point in between D and C. Find the length of DF such that t EF divides the parallelogram into two parts with exactly equal areas.

Ans: Draw the trapezoid.

Let the area of the trapezoid AEFD be A1.

A1 = (1/2) h (AE + DF)

Let ‘h’ be the height of the parallelogram.

Suppose the area of the trapezoid EBCF be A2.

A2 = (1/2) h (EB + FC)

We know,

EB = 20 - 3 = 17 , FC = 20 - DF

We should now substitute EB and FC in

A2 = (1/2) h (EB + FC)

A2 = (1/2)X(h)X(17 + 20 - DF)

we need to have two equal areas A1 and A2 for EF to divide the parallelogram

(1/2)X(h)X(3 + DF) = (1/2)XhX(37 - DF)

On multiplying both sides by 2 and then dividing them by h --

3 + DF = 37 - DF

Solve for DF

2DF = 37 - 3

2DF = 34

DF = 17 cm

**2.** Consider that two ships are sailing on the opposite sides of a lighthouse. The angle of elevation of the highest point of the lighthouse 100m high, when observed from the ships, is 30º and 45º respectively. Find the distance between the two ships.

Ans: Construct a triangle ACD where B is a point on AC and BD be the height of the lighthouse and A and C are the positions of the ships. Then, BD = 100 m, angle BAD = 30° ,angle BCD = 45°

tan 30° = BD/BA

or, BA= 100√3m.

tan 45°=BD/BC

or, BC=100m.

Distance between two ships = BA+BC = 100(1+√3)= 273m.

The term “Geometry” is derived from Greek, where “Geo”refers to “Earth” and “metron” means “measure”.

The Greek words "trigonon" and "metron" when clubbed together form the term “Trigonometry”. Hipparchus, a Greek mathematician invented trigonometry.

FAQ (Frequently Asked Questions)

1. What are the Uses of Trigonometry?

Ans: Trigonometry is an integral part of modern-day mathematics. Trigonometry The applications of trigonometry are spread across various fields such as architecture and surveys, astronomical studies, physics, engineering, and lots more. In construction, trigonometry is used to the height of the building, the width length, etc., and many other such things. In architecture, trigonometry is used to calculate structural load, roof slopes, ground surfaces, including sun shading and light angles. In physics, trigonometry is used to find the vector components , the mechanics models of various waves and oscillations. Trigonometry is utilized in oceanography to calculate the peak of waves in oceans.

2. What are the Uses of Geometry?

Ans: Geometry has lots of practical uses in daily life, such as measuring the circumference, area, and volume, when one needs to build something. Geometric shapes also play an integral role in common activities, such as video games and sports. Geometry is instrumental in the field of engineering and architecture. Art consists of the formation of figures & shapes, a basic understanding of the two-dimensional and three-dimensional figures which include basic knowledge about spatial concepts. Thus geometry also has great applications in the field of art and craft. The creation of shapes is a result of the use of geometrical forms like circles, triangles, mandalas, etc.