550 p w 440 p w 990 2p p 495 550 p 495 550 p w. 14952 w 55 w 5. Applications Involving Geometry Solving a Geometry Application Example 5 The sum of the two acute angles in a right triangle is 90.The measure of one angle is 6 less than 2 times the measure of the other angle.Find the measure of each angle. Solution: Let x represent one acute angle. Let y represent the other acute angle. The sum of the two acute angles is 90 One angle is 6 less than 2 times the other angle y x y 90 x 2y 6 x Because one variable is already isolated, we will use the substitution method. x y 90 x 2y 6 12y 62 x 2y 6 y 90 Substitute into the first equation. 3y 6 90 3y 96 y 32 x 2y 6 y 32 To find x, substitute into the equation x 21322 6 x 64 6 x 58 x 2y 6. The two acute angles in the triangle measure 32 and 58. Skill Practice 5. Two angles are supplementary.The measure of one angle is 16° less than 3 times the measure of the other. Use a system of equations to find the measures of the angles. Answers 4. The speed of the plane is 540 mph, and the speed of the wind is 60 mph. 5. The angles are 49° and 131°. Add the equations. Substitute into the equation Solve for w. The speed of the plane in still air is 495 mph, and the speed of the wind is 55 mph. Skill Practice 4. A plane flies 1200 mi from Orlando to New York in 2 hr with a tailwind.The return flight against the same wind takes 2.5 hr. Find the speed of the plane in still air and the speed of the wind. ¶ Section 3.4 Applications of Systems of Linear Equations in Two Variables 265
miller_intermediate_algebra_4e_ch1_3
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