Explanation Definition used: The sum of 3 angles in a triangle is 180 ° . Since one of the angle in a right triangle is 90 ° , the sum of other two angle is 90 ° . Therefore, those angles are acute angles, they are also called as complementary angles. Formula used: Let A be an acute angle of a right triangle. Then the six trigonometric functions of A are as follows. sin A = side opposite A hypotenuse , cos A = side adjacent A hypotenuse , tan A = side opposite A side adjacent A , csc A = hypotenuse side opposite A , sec A = hypotenuse side adjacent A , cot A = side adjacent A side opposite A Procedure used: To solve a right triangle: “1. Sketch the right triangle and label the known and unknown sides and angles. 2. Express each of the three unknown parts in terms of the known parts and solve for the unknown parts. 3. Check the results. The sum of the angles should be 180 ° . If only one side is given, check the computed side with the Pythagorean theorem. If two sides are given, check the angles and computed side by using appropriate trigonometric functions.” Calculation: Consider a right triangle with the acute angles A and B and right angle C . The sides opposite to these angles can be named as a , b and c respectively. So, c is the hypotenuse of the right triangle. Given that, B = 37.5 ° and a = 0.862 . Sketch the right triangle with the known measures as shown below in Figure 1. By the above definition, the sum of the angle A and B is 90 ° . Therefore, A + B = 90 ° A + 37

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Chapter 4.4, Problem 19E

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To solve: The right triangle if B=37.5° and a=0.862.

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Chapter 4.4, Problem 18E

Chapter 4.4, Problem 20E

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Chapter 4 Solutions

Basic Technical Mathematics

Ch. 4.1 - Change 17°24′ to decimal form. Ch. 4.1 - Prob. 2PE Ch. 4.1 - Prob. 3PE Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E

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The right triangle if B = 37.5 ° and a = 0.862 .

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