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Terms used in Heights and Distances Back to Top

Applications of TrigonometryGenerally in grade nine, students are introduced to a branch of mathematics whichbecomes very useful in real life problems. This branch is known as trigonometry. Theword "trigonometry" is composed of two Greek language words - "trigonon" and"metron" where, former means "triangle" and the latter indicates "measure".Trigonometry is a subject which deals with sides, angles and triangles. It majorlyconcerns with the ratio between the sides and angles of a right-angled triangle.

In this page, we are going to discuss about the Applications of Trigonometry.Trigonometry is used in surveying and to determine Heights and Distances. Innavigation, it is to determine the location and the distances and in the fields likenondestructive testing for determining things such as the angle of reflection orrefraction of an ultrasound wave. The trigonometrical phenomena are even used asdiverse fields as mechanical engineering, physics, electrical engineering, astronomy,music, biology and ecology.

Tutorvista provides online help for the students who are willing to learn real lifeapplications of trigonometry. Our tutorials are full of knowledge and our online tutorsare quite happy to solve your queries about applications of trigonometry. So, go aheadwith us and learn about trigonometrical real life applications.

Below we can see terms used in the applications of trigonometry:

Horizontal Ray:

A ray parallel to the surface of the earth emerging from the eye of the observer isknown as horizontal ray.

Ray of Vision:

The ray from the eye of the observer towards the object under observation is known asthe ray of vision or ray of sight.

Angle of Elevation:

If the object under observation is above the horizontal ray passing through the point ofobservation, the measure of the angle formed by the horizontal ray and the ray ofvision is known as angle of elevation.

Angle of Depression: If the object under observation is below the horizontal ray

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Real Life Applications of Trigonometry Back to Top

passing through the point of observation, the measure of the angle formed by thehorizontal ray and the ray of vision is known as angle of depression.

Given below are some of the real world applications of trigonometry. Trigonometry isthe branch of mathematics that studies triangles and their relationships. Trigonometryis commonly used in finding the height of towers, mountains and also used to find thedistance of the shore from a point in the sea etc. Trigonometry provides perspectiveon real world events. It is used in satellite systems and astronomy, architecture,engineering, geography and many other fields.

Applications of Trigonometry in Engineering

Trigonometry is the relationships between the sides and angles of triangles. Suchrelationships are involved in a wide range of engineering problems. Engineers ofvarious types use the fundamentals of trigonometry to design bridges, build structuresand solve scientific problems. Trigonometry is very important with engineers who dealwith waves, magnetic and electric fields.

Applications of Trigonometry in Astronomy

Trigonometry is used by astronomers to calculate the distance to the stars.Trigonometry to measure distances between universe objects are at greater distances.

Applications of Trigonometry in Architecture

In architecture, trigonometry plays a massive role in the compilation of building plans.Trigonometry is used for the designing of a building to predetermine geometricalpatterns and how much material and labor will required in order to erect a structure.

Given below are some of the examples in calculating heights and distances:

Solved Examples

Question 1: From a cliff 150m above the shore line, the angle of depression

of a ship is 190 30'. Find the distance from the ship to a point on the shoredirectly below the observer.Solution:

Let OB be the cliff of height 150 m, A be the position of the ship the

angle of depression of the ship is 19 0 30'.

In Right angled triangle AOB, OA = adjacent side, OB = oppositeside = 150 m

∠

OA OA

Cot (19 0 30') = =

OA = 150 Cot (19 0 30') = 150 tan (90 - 19 0 30')

OA = 150 * tan (70 0 30') = 150 (2.8239) = 423.59 m

Hence, the distance from the ship to a point on the shore is 423.59m.

Question 2: A person standing on the bank of a river observers that the

angle of elevation of the top of a tree standing on the opposite bank is 60 0.When he was 40m away from the bank he finds that the able of elevation to

be 30 0. Find the (i) height of the tree, (ii) The width of the river, correct totwo decimal places.Solution:

Let CD is the tree, CD = h m high and BC is the river, BC = x.

The observer is standing at A, From figure DAC = 300 and DBC

= 600.

Step 1:In right angled BCD, x is the adjacent side, h is the opposite side.

tan 60 0 = => =

=

x = h ---------------------------(1)

Step 2:

From right angled ACD, tan 300 =

Here, AC = AB + BC = 40 + x

=

x + 40 = h ----------------------------(2)

Step 3:Plugging in value of h from (1) in (2)

x + 40 = ( x)

x + 40 = 3x

2x = 40

x = 20 (Divide each side by 2)

Now

(1) => h = x = 1.732 (20) = 34.64 [ = 1.732 ]

h = 34.64

The height of the tree = 34.64 m, width of the river = 20 m

OAOB

OA150

∠ ∠

∠

DCBC

3√DCBC

3√hx

3√

∠DCAC

13√

hx+40

3√

3√ 3√

3√ 3√

◀◀ Sine and Cosine De Moivre's Theorem ▶▶

More topics in Applications of Trigonometry

Angle of Depression Angle of Elevation

Line of Sight

Related Topics

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