# Trigonometry Word Problems

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Trigonometry is an important branch of mathematics which deals with ratios and relationships between angles and sides of triangles, especially right angled triangles. Trigonometry deals with mainly six types of trigonometric ratios which are – sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec) and cotangent (cot). There are various important formulae which are used in trigonometry and numerous word problems. Trigonometry word problems include problems relating to circles, degrees, trigonometric functions, radians, exact values of trigonometric ratios and problems involving identities. Students usually find it difficult while solving trigonometrical word problems.

## Solving Trigonometry Word Problems

## Right Triangle Trigonometry Word Problems

### Solved Examples

Let OA be the height of the light house and B be the position of boat.

Given, $\angle$ OBA = 15 degrees and OA = 60 m

or OB = OA cot 15 o (cot x = $\frac<1>

or OB = 60 cot (45 – 30)

Here BC = 100 mt, $\angle$ BAC = 45 degree and $\angle$ BAD = 60 degree

Let the length of the CD = x mt

In Triangle ABC

Now, in triangle ABD,

Therefore, BD = BC + CD

=> 100 $\sqrt 3$ = 100 + x

or x = 100( $\sqrt 3$ – 1) mt

Hence the height of the CD is 100( $\sqrt 3$ – 1) mt .