Trigonometry: Calculating Lengths and Angles in Right-Angled Triangles
This page provides a detailed explanation of trigonometric concepts and methods for calculating lengths and angles in right-angled triangles. The content is structured into two main sections: methodology for calculating lengths and methodology for calculating angles.
The first section focuses on how to calculate a side of a right-angled triangle with one measurement. It introduces the SOHCAHTOA mnemonic, which helps remember the trigonometric ratios: Sine, Cosine, and Tangent.
Vocabulary: SOHCAHTOA - A mnemonic device for remembering trigonometric ratios: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent.
An example is provided using a right-angled triangle ABC, where the angle BAC is 30°, and the adjacent side BC is 8 cm. The problem demonstrates how to find two sides of a right-angled triangle using cosine and tangent functions.
Example: To find AC hypotenuse, use cosine: AC = 8 / cos 30° = 9.2 cm. To find AB opposite, use tangent: AB = 8 × tan 30° = 4.6 cm.
The second section explains the methodology for calculating an angle in a right-angled triangle. It uses an example where two sides of a right-angled triangle are given 5cmand12cm, and the task is to find the measure of an angle.
Highlight: The inverse trigonometric functions arcsin,arccos,arctan are used to calculate angles when side lengths are known.
The document emphasizes the importance of using a calculator for these calculations, especially when dealing with inverse trigonometric functions.
Definition: Inverse trigonometric functions alsocalledarcfunctions are used to find an angle when given a trigonometric ratio.
This comprehensive guide provides students with the necessary tools to calculate the length of a side in a right-angled triangle with one measurement and an angle, as well as to calculate the measure of an angle in a right-angled triangle using trigonometric ratios.