How to Solve Trigonometry Problems Step by Step for Beginners

Courtney

12/10/2025

Maths

What is Trigonometry and how to solve it

Subjects

Maths

Geometry and measure

Angles, lines and polygons

Triangles

388

•

12 Oct 2025

•

4 pages

How to Solve Trigonometry Problems Step by Step for Beginners

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Courtney

@courtney01

Trigonometry is a branch of mathematics dealing with relationships between... Show more

1 / 4

Opposite
# Trigonometry

Angie

Hypotenuse

Adjacent

# Steps:
1. Label the triangle
2. Pich correct Formula
3. Set up the equation
4. Sove

Finding Missing Sides Using Trigonometry

This page demonstrates how to solve trigonometric equations with sin and cos to find missing sides in a right-angled triangle.

Example: To find the opposite side (x) in a triangle with hypotenuse 12m and angle 35°:

Identify the given information: angle = 35°, hypotenuse = 12m
Choose the appropriate formula: Sin θ = Opposite / Hypotenuse
Set up the equation: Sin 35° = x / 12
Solve for x: x = 12 × Sin 35° = 6.88 (rounded)

Highlight: When solving for a side, multiply if the known side is in the denominator of the ratio, and divide if it's in the numerator.

Using Tangent to Find Missing Sides

This section explains how to solve trigonometric ratios using the tangent function to find missing sides in a right-angled triangle.

Example: To find the adjacent side (x) in a triangle with opposite side 15m and angle 18°:

Identify the given information: angle = 18°, opposite = 15m
Choose the appropriate formula: Tan θ = Opposite / Adjacent
Set up the equation: Tan 18° = 15 / x
Solve for x: x = 15 / Tan 18° = 13.51 (rounded)

Highlight: When solving for the adjacent side using tangent, divide the opposite side by the tangent of the angle.

Finding Missing Angles in Trigonometry

This page covers how to solve trigonometric equations to find missing angles in a right-angled triangle.

Steps to find a missing angle:

Label the sides of the triangle
Identify the known sides
Choose the appropriate trigonometric ratio
Set up the equation and solve for the angle using inverse trigonometric functions

Example: To find angle x in a triangle with adjacent side 3cm and hypotenuse 8cm:

Identify the given information: adjacent = 3cm, hypotenuse = 8cm
Choose the appropriate formula: Cos x = Adjacent / Hypotenuse
Set up the equation: Cos x = 3 / 8
Solve for x using inverse cosine: x = Cos⁻¹ $3/8$ = 67.98° (rounded)

Highlight: Use a calculator to solve trigonometric equations involving inverse functions like Cos⁻¹, Sin⁻¹, or Tan⁻¹.

Introduction to Trigonometry

Trigonometry is the study of relationships between angles and sides in right-angled triangles. This page introduces the fundamental concepts and steps for solving trigonometry problems easily.

The three main steps to solve trigonometric problems are:

Label the triangle
Pick the correct formula
Set up and solve the equation

Vocabulary:

Hypotenuse: The longest side of a right-angled triangle, opposite the right angle
Opposite: The side opposite to the angle in question
Adjacent: The side next to the angle in question

Definition: SOH CAH TOA is a mnemonic device used to remember the trigonometric ratios:

Sin θ = Opposite / Hypotenuse
Cos θ = Adjacent / Hypotenuse
Tan θ = Opposite / Adjacent

Highlight: Trigonometry is used to calculate missing sides or angles in right-angled triangles.

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David K

iOS user

Sudenaz Ocak

Android user

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Greenlight Bonnie

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Rohan U

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Elisha

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Paul T

iOS user

Subjects

Maths

Geometry and measure

Angles, lines and polygons

Triangles

Maths

12 Oct 2025

388

4 pages

How to Solve Trigonometry Problems Step by Step for Beginners

Courtney @courtney01

Trigonometry is a branch of mathematics dealing with relationships between side lengths and angles of triangles. This guide covers the basics of solving trigonometric problems step by step for beginners... Show more

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Finding Missing Sides Using Trigonometry

This page demonstrates how to solve trigonometric equations with sin and cos to find missing sides in a right-angled triangle.

Example To find the opposite side (x) in a triangle with hypotenuse 12m and angle 35°

Identify the given information angle = 35°, hypotenuse = 12m

Choose the appropriate formula Sin θ = Opposite / Hypotenuse

Set up the equation Sin 35° = x / 12

Solve for x x = 12 × Sin 35° = 6.88 (rounded)

Highlight When solving for a side, multiply if the known side is in the denominator of the ratio, and divide if it's in the numerator.

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Using Tangent to Find Missing Sides

This section explains how to solve trigonometric ratios using the tangent function to find missing sides in a right-angled triangle.

Example To find the adjacent side (x) in a triangle with opposite side 15m and angle 18°

Identify the given information angle = 18°, opposite = 15m

Choose the appropriate formula Tan θ = Opposite / Adjacent

Set up the equation Tan 18° = 15 / x

Solve for x x = 15 / Tan 18° = 13.51 (rounded)

Highlight When solving for the adjacent side using tangent, divide the opposite side by the tangent of the angle.

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Improve your grades

Join milions of students

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Finding Missing Angles in Trigonometry

This page covers how to solve trigonometric equations to find missing angles in a right-angled triangle.

Steps to find a missing angle

Label the sides of the triangle

Identify the known sides

Choose the appropriate trigonometric ratio

Set up the equation and solve for the angle using inverse trigonometric functions

Example To find angle x in a triangle with adjacent side 3cm and hypotenuse 8cm

Identify the given information adjacent = 3cm, hypotenuse = 8cm

Choose the appropriate formula Cos x = Adjacent / Hypotenuse

Set up the equation Cos x = 3 / 8

Solve for x using inverse cosine x = Cos⁻¹ $3/8$ = 67.98° (rounded)

Highlight Use a calculator to solve trigonometric equations involving inverse functions like Cos⁻¹, Sin⁻¹, or Tan⁻¹.

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Introduction to Trigonometry

Trigonometry is the study of relationships between angles and sides in right-angled triangles. This page introduces the fundamental concepts and steps for solving trigonometry problems easily.

The three main steps to solve trigonometric problems are

Label the triangle

Pick the correct formula

Set up and solve the equation

Vocabulary

Hypotenuse The longest side of a right-angled triangle, opposite the right angle

Opposite The side opposite to the angle in question

Adjacent The side next to the angle in question

Definition SOH CAH TOA is a mnemonic device used to remember the trigonometric ratios

Sin θ = Opposite / Hypotenuse

Cos θ = Adjacent / Hypotenuse

Tan θ = Opposite / Adjacent

Highlight Trigonometry is used to calculate missing sides or angles in right-angled triangles.