Extra Practice for Sem 2, Quiz 6

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form I have the short leg, so to get long leg, multiply by √3 x 30 5√3 60 5

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form I have a leg, so to get the hyp, multiply by √2 45 x 16√2 45 16

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form x 30 I have the hyp, so get short leg first by dividing by 2 9 18 60 Then, from the short leg to get the long leg, multiply by √3

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form 9√3 x I have the hyp, so get short leg first by dividing by 2 30 9 18 60 Then, from the short leg to get the long leg, multiply by √3

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form 7√2 I have the hyp, so get short leg first by dividing by 2 60 Then, from the short leg to get the long leg, multiply by √3 7√6 x 14√2 30

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form 6√3 I have the hyp, so get short leg first by dividing by 2 60 Then, from the short leg to get the long leg, multiply by √3 18 x 12√3 30 6√3•√3 = 6•3 = 18

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form I have the long leg, so get short leg first by dividing by √3 48 60 Then, from the short leg to get the hyp, multiply by 2 48√3 96 x 30

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form I have the long leg, so get short leg first by dividing by √3 8√2 60 Then, from the short leg to get the hyp, multiply by 2 8√6 16√2 30 √2 8√6 √3 = 8√2

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form I have the long leg, so get short leg first by dividing by √3 6√3 60 Then, from the short leg to get the hyp, multiply by 2 18 x 12√3 30 18 √3 • √3 = 18√3 3 = 6√3

Use special right ∆ rules to find the exact value of x Use special right ∆ rules to find the exact value of x. Answers in simplified radical form I have the hyp, so to get the legs, divide by √2 45 4√6 x 4√3 √3 4√6 √2 = 4√3 45

Use Soh Cah Toa to find the value of x. Round to the nearest tenth. 33 cos(x) = 27/33 x = cos-1 (27/33) x = 35.1 x 27

Use Soh Cah Toa to find the value of x. Round to the nearest tenth. sin (20) = 80 1 x x = 80 sin (20) x = 233.9 x 80 20

Use Soh Cah Toa to find the value of x. Round to the nearest tenth. tan (29) = x 1 17 x = 17tan (29) x = 9.4 29 17 x

Use Soh Cah Toa to find the value of x. Round to the nearest tenth. cos(x) = 97/133 x = cos-1 (97/133) x = 43.2 x 133 97

Use Soh Cah Toa to find the value of x. Round to the nearest tenth. sin (65) = x 1 41 x = 41sin (65) x = 37.2 41 65 x

Use Soh Cah Toa to find the value of x. Round to the nearest tenth. tan(x) = 24/10 x = tan-1 (24/10) x = 67.4 x 10 24

Use Soh Cah Toa to find the value of x. Round to the nearest tenth. cos(72) = 18 1 x x = 18 cos(72) x = 58.2 72 x 18

Use Pythagorean Thm to find the value of x. Round to the nearest tenth. 18 24

Use Pythagorean Thm to find the value of x. Round to the nearest tenth. 50 x 48

Use Pythagorean Thm to find the value of x. Round to the nearest tenth. 20 x 12

Use Altitude-on-hypotenuse theorems to find the value of x Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth. x = 5 5 10 10x = 25 x = 2.5 5 x 10

Use Altitude-on-hypotenuse theorems to find the value of x Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth. x = 3 3 5 5x = 9 x = 1.8 3 x 5

Use Altitude-on-hypotenuse theorems to find the value of x Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth. x = 8 8 x + 12 x2 + 12x = 64 x2 + 12x – 64 = 0 (x – 4)(x + 16) = 0 x = 4 x = -16 x 8 12

x 6 5 x = 6 6 x + 5 x2 + 5x = 36 x2 + 5x – 36 = 0 (x – 4)(x + 9) = 0 Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth. x = 6 6 x + 5 x2 + 5x = 36 x2 + 5x – 36 = 0 (x – 4)(x + 9) = 0 x = 4 x = -9 x 6 5

Use Altitude-on-hypotenuse theorems to find the value of x Use Altitude-on-hypotenuse theorems to find the value of x. Round to the nearest tenth. 92 + 122 = x2 x2 = 81 + 144 x2 = 225 x = 15 9 x 12

Factor. x2 + 12x + 32 (x + 4)(x + 8)

Factor x2 – 12x + 32 (x – 4)(x – 8)

Factor x2 – 4x + 32 (x + 4)(x – 8)

Factor x2 + 14x + 45 (x + 9)(x + 5)

Factor x2 + 15x + 36 (x + 12)(x + 3)

I am standing on the ground looking up at the top of a building at an angle of elevation of 75˚. If I am currently 40’ from the door, how tall is the building? tan (75) = x 1 40 x = 40tan (75) x = 149.3’ x 40 75˚

I am standing at the top of a building, looking at an ice cream truck at an angle of depression of 48˚. If the distance from me to the ice cream truck is 64yds, how far is the ice cream truck from the building? cos (48) = x 1 64 x = 64cos(48) x = 42.8yds x 64 48˚

I am looking down into the ocean, and I see a shark exactly 20 feet from me. If the shark is 15 feet below the surface of the water, what is the angle of depression at which I see him? sin(x) = 15/20 x = sin-1 (15/20) x = 48.6 20 15 x˚