Using the distance formula Using formulas to solve unknowns. Pythagorean Theorem. Finding Legs of Right Triangles

Transcription

1 Math 154 Chapter 9.6: Applications of Radical Equations Objectives: Finding legs of right triangles Finding hypotenuse of right triangles Solve application problems involving right triangles Pythagorean Theorem Using the distance formula Using formulas to solve unknowns Finding Legs of Right Triangles Ex: Find the missing leg by using the Pythagorean Theorem, a b c. x Answer: 8 = the missing leg 1. Find the missing leg by using the Pythagorean Theorem, a b c. x 6 10 Answer: 4 = the missing leg

2 Finding Hypotenuses of Right Triangles Ex: Find the missing hypotenuse by using the Pythagorean Theorem, a b c x Answer: 5 = the missing hypotenuse 1. Find the missing hypotenuse by using the Pythagorean Theorem, a b c. 8 x 6 Answer: 10 feet = the missing hypotenuse

3 Application Problems Involving Right Triangles Ex: Find the length of the diagonal of a rectangle with length of 10 inches and width 9 inches. Round your answer to the nearest hundredth. Answer: inches = the diagonal 1. The diagonal of a rectangle is 5 inches and the width is 15 inches. Find the length of the rectangle. Answer: 0 inches = the length of the rectangle

4 Application Problems Involving Right Triangles Ex: If a 7.5 foot ladder is placed 4.5 feet from the base of a building, how far up the wall will it reach? Answer: 6 feet = how far up the wall the ladder reaches 1. A 14 foot tree is supported by ropes. One rope goes from the top of the tree to a point on the ground 6 feet from the base of the tree. Find the length of the rope. Round your answer to the nearest hundredth. Answer: 15.3 feet = the length of the rope

5 Distance Formula Finding the Distance Between Points on a Graph Ex: Find the distance between the points (1, ) and (5, 5) using the distance formula. d distance ( ) ( ) change in x squared change in y squared Answer: 5 = the distance between (1, ) and (5, 5) 1. Find the distance between the points (-1, -) and (4, -5) using the distance formula. d distance ( ) ( ) change in x squared change in y squared Answer: = the distance between the points (-1, -) and (4, -5)

6 Using Formulas to Find Unknowns Ex: Find the radius of a circle whose area is 60 square feet using the area formula, where A r, Let r = the radius area 3.14 times radius squared Answer: about 4.37 feet = the radius of the circle 1. Find the radius of the cone whose volume is 60 cube feet using the volume formula, V r h, where and h 4. Let r = the radius area 3.14 times radius squared times height Answer: about.19 feet = the radius of the cone

7 . A square has an area of 5 square meters. Determine the length of each side. area side squared s A s s Answer: 15 meters = the side of the square 3. The length of a diagonal, d, for a rectangular solid is d l w h, where l is the length, w is the width, and h is the height. Find the length of the diagonal for a rectangular solid if the length is inches, the width is 3 inches, and the height is 4 inches. diagonal length ( ) ( ) ( ) square root of length squared plus width squared plus height squared Answer: = the length of the diagonal

8 4. The period or time, T, it takes (in seconds) for a pendulum to swing back and forth is L T, where 3. 14, L is the length of the pendulum in feet, and g is acceleration due g to gravity (3 feet per second squared). Find the period of a pendulum if it s length is16 feet. period ( ) times 3.14 times the square root of length divided by 3 Answer: about 4.44 sec = the period of the pendulum 5. The velocity of a falling object, v, (in feet per second) is v gh, where h is the height in feet for which the object falls, and g is acceleration due to gravity (3 feet per second squared). Find the velocity of an object that has dropped16 feet. velocity square root of times 3 times 16 Answer: 3 ft/sec = the velocity of the falling object