# Trigonometric Ratios Worksheet Answers

March 4, 2024

A branch of mathematics called trigonometry. It studies the relationships between triangular dimensions and degrees.

The Greek words trigonon, “triangle,” and metron, “measure,” combine to form the word trigonometry. In the third century BC, the Hellenistic civilization gave birth to science. through the use of geometry in astronomical studies. While Indian scholars created the earliest tables of figures. They are for trigonometric ratios worksheet answers. It is also known as trigonometric operations as a sine. The Greeks focused on chord computations.

Throughout the past, trigonometry has been in geography, mapping, space mechanics, and sailing. There are several alternatives for trigonometry. Trigonometric solutions are rewritten using these trigonometric equations to make them simpler. Find a more practical way to express them, or work out a formula. Sine, cos, tan, cosec, sec, and cot are six crucial trigonometric operations. The trigonometry-related questions will be in this post.

## What Do You Understand by the Word Trigonometry?

Thought to be one of the most crucial areas of maths is trigonometry. Trigonometry is a term that fuses the words “trigonon” and “metron.” It is the examination of how a right triangle’s sides and angles interact. Utilizing methods and opinions, aids in identifying and assessing the right-angled triangle’s unknown sizes. In the basics of trigonometry, angles measured, and problems involving angles. Sine, cosine, and tangent are the three fundamental operations of trigonometry. These three fundamental ratios or functions cotangent, secant, and cosecant—can be to construct further significant trigonometric equations. The fundamental ideas of trigonometry are upon these parameters.

## Father of Trigonometry

The study of the correlations between triangular side dimensions and angles is trigonometry. Hipparchus is the inventor of trigonometry. The Greek mathematical expert Hipparchus discovered trigonometry in the second decade BC. He created the first trigonometric table to resolve several circular trigonometric problems.

## What are Trigonometric Ratios?

The values of each trigonometric operator are as ratios. They are focusing on the right-handed triangle’s edge trigonometric ratio worksheets. A right-angled triangle’s side lengths in relation to any of its acute vertices. They are to as a specific angle’s trigonometric ratios. The right triangle’s three sides are as follows:

- The broadest side is the hypotenuse.
- Side that is perpendicular to the right angle
- The bottom side that runs parallel to the angle

## How to Find Trigonometric Ratios?

The corresponding trigonometric equations, where a, b, and c are the lengths of the sides. They are in the preceding illustration. They are to the known angle A to produce these ratios:

- The sine value (sin) is the ratio of the side across from the position to the hypotenuse.

\(Sin A= \dfrac{Opposite Side}{Hypotenuse Side}\) = \(\dfrac{a}{c}\)

- The cosine value is the ratio between the hypotenuse and the neighboring side. It is the part of the triangle related to the right angle.

\(Cos A= \dfrac{Adjacent Side}{Hypotenuse Side}\) = \(\dfrac{b}{c}\)

- The tangent value is the proportion of the opposing leg to the adjoining line.

\(Tan A= \dfrac{Opposite Side}{Adjacent Side}\) = \(\dfrac{a}{b}\)

The hypotenuse of a right triangle is the side that faces away from the \(90\)-degree curve. It is the largest half of the triangle. One of the two sides that are to angle A and the neighboring leg is to the side of angle A. The opposing side is to as being perpendicular to angle A. The terms perpendicular and base are to describe the reverse and neighboring sides.

## Table Formula for Trigonometry

\( 0º \) | \( 30º \) | \( 45º \) | \( 60º \) | \( 90º \) | |

\( sin \) | \( 0 \) | \( \dfrac{1}{2} \) | \( \dfrac{1}{\sqrt{2}} \) | \( \dfrac{\sqrt{3}}{2} \) | \( 1 \) |
---|---|---|---|---|---|

\( cos \) | \( 1 \) | \( \dfrac{\sqrt{3}}{2} \) | \( \dfrac{1}{\sqrt{2}} \) | \( \dfrac{1}{2} \) | \( 0 \) |

\( tan \) | \( 0 \) | \( \dfrac{1}{\sqrt{3}} \) | \( 1 \) | \( \sqrt{3} \) | undefined |

\( cosec \) | undefined | \( 2 \) | \( \sqrt{2} \) | \( \dfrac{2}{\sqrt{3}} \) | \( 1 \) |

\( sec \) | \( 1 \) | \( \dfrac{2}{\sqrt{3}} \) | \( \sqrt{2} \) | \( 2 \) | undefined |

\( cot \) | undefined | \( \sqrt{3} \) | \( 1 \) | \( \dfrac{1}{\sqrt{3}} \) | \( 0 \) |

## Uses of Trigonometric Ratios

The following are a few uses for trigonometry:

- Determining the peaks of large mountains or skyscrapers
- Calculating the length between the beach and the sea
- Measurement of the separation between two heavenly bodies
- Calculating the output of power from solar cells at various orientations
- Expressing several physical parameters, including electromagnetic and mechanical motions, etc.

## Trigonometric Worksheet Answers

**Example 1: A man is looking at a tree that is \(57\) feet tall. He determined that the tree’s shadow was \(26\) feet long. Can you assist him in estimating the angle of altitude of the sun from the top of the shadow?**

**Solution**:

Let x be the angle of height so,

\(tan x= \dfrac{57}{26}= 2.1923\)

\( x= tan^{-1}(2.1923)\)

Or \(x= 65.4\) degree

**Example 2: If the hypotenuse of a right-angled triangle ABC is 5 cm, the base is 3 cm, and the perpendicular is 4 cm, and if ACB =, then determine the tan, sin, and cos angles.**

**Solution**:

Given values

Hyp. AC= \(5\) cm

Base BC= \(3\) cm

Perp. AB= \(4\) cm

tan = \(\dfrac{4}{3}\)

sin = \(\dfrac{4}{5}\)

cos = \(\dfrac{3}{5}\)

## Final Words

The connection is using trigonometric ratios. Such as sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometric ratios worksheet answers have been throughout the piece. It is how to calculate them and how to solve a few related issues. Learners may access the site to learn more about trigonometry and associated topics. We have provided detailed explanations.

## FAQS

SOH CAH TOA: What is it?

The acronym SOH CAH TOA can be used to recall the trigonometric ratios equation so that:

SOH: The proportion of the opposite side to the hypotenuse is the sine function.

CAH: Cosine is a function of the side nearest to the hypotenuse, or CAH.

TOA: The ratio of the opposing and neighboring sides is known as the tangent.

What connection does there exist between sin, cos, and tan?

The relationship of the sine and cosine functions is what determines tangent functions.

Tan equals \( \dfrac{sin}{cos}\).

How are cotangent, secant, and cosecant calculated?

The cotangent is the base/perpendicular ratio of the next and divergent sides.

Hypotenuse to neighboring side ratio is known as secant (Hypotenuse/Base).

The cosecant (Hypotenuse/Perpendicular) is the percentage of the hypotenuse to the opposing side.

How can you determine which is near or opposite?

The portion that is other than the angle you are attempting to solve for is known as the opposing side. The end next to the angle you are calculating for is the neighboring side.

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