To calculate the angle of a right triangle, sine cosine tangent formula is used. The ratio of the different sides of the triangle gives the sine, cosine, and tangent angles. Here, the hypotenuse is the longest side, the side opposite to the hypotenuse is the opposite side and the where both the sides rest is the adjacent side. A right angle looks like this:

## Formulas for Sine, Cos, Tan

The **Sine Cosine Tangent Formula** is,

Angle Name | Angle Formula |
---|---|

Sine Angle Formula | Sin θ = Opposite side ⁄Hypotenuse |

Cos Angle Formula | Cos θ = Adjacent side⁄Hypotenuse |

Tangent Angle Formula | Tan θ = Opposite Side ⁄Adjacent Side |

## Solved Examples

**Question 1: Calculate the angle in a right triangle whose adjacent side and hypotenuse are 12 cm and 20 cm respectively?**** Solution:**

Given,

Adjacent side = 12 cm

Hypotenuse = 20 cm

cos θ = Adjacent⁄Hypotenuse

cos θ = 12⁄20

θ = cos^{−1}(0.6)

θ = 53.13

**Question 2: If sin A = 21/29 and cos A = 20/ 29, then find the value of tan A.**

Solution:

Given,

sin A = 21/29

cos A = 20/29

We know that,

sin θ = Opposite/Hypotenuse

cos θ = Adjacent/Hypotenuse

Thus,

Opposite = 21

Adjacent = 20

Hypotenuse = 29

Therefore, tan A = Opposite/Adjacent

= 21/20

**Question 3: If sin A = ⅗, then find the value of cos A and tan A.**

Solution:

Given,

sin A = Opposite/Adjacent = ⅗

By Pythagoras theorem,

(Hypotenuse)^{2} = (Opposite side)^{2} + (Adjacent side)^{2}

5^{2} = 3^{2} + (Adjacent side)^{2}

(Adjacent side)^{2} = 25 – 9 = 16

Adjacent side = √16 = 4

Therefore,

cos A = Adjacent/Hypotenuse = ⅘

tan A = Opposite/Adjacent = ¾

More topics in Sine Cosine Tangent Formulas | |
---|---|

Sine Formula | Cosine Formula |

Tangent Formula | Arctan Formula |

Half Angle formula | Double Angle Formulas |