Home
Math symbols
Jokes
Forum
About us
Links
Contact us
Site map
Search The Site
   
   Program of Lessons
 
 Study Guide
 Topics of problems
 Tests & exams
www.bymath.com Study Guide - Arithmetic Study Guide - Algebra Study Guide - Geometry Study Guide - Trigonometry Study Guide - Functions & Graphs Study Guide - Principles of Analysis Study Guide - Sets Study Guide - Probability Study Guide - Analytic Geometry Select topic of problems Select test & exam Rules Price-list Registration

Solving of right-angled triangles

Solving of right-angled triangles:
by two sides, by a side and an acute angle.

 1. By two sides. If two sides of a right-angled triangle are given, then the third side can becalculated by the Pythagorean theorem ( see the paragraph of the same name in the section "Triangle" of the part "Geometry" ). Acute angles are determined by one of the three firstformulas for trigonometric functions, depending on the fact what sides are known. Forinstance, if legs  a and  b are given, then angle A is determined by the formula:


tan A = a / b .

E x a m p l e  1. A leg a = 0.324, a hypotenuse c = 0.544. Find the second leg band the angles A and B.
S o l u t i o n . The leg  b  is equal:
E x a m p l e  2. Two legs are given: a = 7.2 cm,  b = 6.4 cm. Find a hypotenuse and the angles A and B.
S o l u t i o n . The hypotenuse c  is equal:
 2. By a side and an acute angle. If one acute angle A is given, then another acute angle B is found as: B = 90 – A . Sides are found by formulas of trigonometric functions, rewritten as:

a = c sin A ,  b = c cos A ,  a = b tan A ,

b = c sin B ,  a = c cos B ,  b = a tan B .

It is necessary to select the formulas, containing a given or already found side.
E x a m p l e. Given:  hypotenuse c = 13.65 m and acute angle A = 5417.Find another  acute angle B and legs  a  and  b .

Back


| Home | About us | Links | Contact us |

Copyright 2002-2012 Dr. Yury Berengard. All rights reserved.