Special Right Triangles Worksheet Answers

1. Geo/Trig 8-1 and 8-2 Practice Name: Date: A. Simplify the following square root expressions. sqrt(4.15) = 2sqrt(15) 1. sqrt(18) 6. 3sqrt(80) 11. sqrt(2/7) = (sqrt(2))/(sqrt(7)) * (sqrt(7))/(sqrt(7)) 5sqrt(9 * 6) 10sqrt(6) 7.5sqrt(24) ما sqrt(3varphi) 9sqrt(3) * sqrt(27) 9 8sqrt(2) 24sqrt(12) B. Set up and solve an equation using the Pythagorean Theorem to find the value of x. 3. 2. 9 X 15 5 4. 6 3 81 sqrt^2 x = overline i149 9 ^ 2 + x ^ 2 = 15 ^ 2 x ^ 2 = 225 5. 6. 7. 2 1 5 5 ^ 2 + 5 ^ 2 = x ^ 2 sqrt(50) = sqrt(x ^ 2) 25 + 25 = x deg 5sqrt(2) = x 3 ^ 2 + x ^ 2 = 6 ^ 2 9 + x ^ 2 = 36 x = 3sqrt(3) sqrt(x ^ 2) = sqrt(27) 8. 12 1 12 8 1 ^ 2 + x ^ 2 = (sqrt(2)) ^ 2 1 + x ^ 2 = 2 sqrt(x ^ 2) = sqrt(1) 1/4 + x ^ 2 = 8sqrt(3) * 8sqrt(3) 144 + x ^ 2 = 192 144 + x ^ 2 = 64 * 3 sqrt^2 x = sqrt(48) x = 4sqrt(3) 12 ^ 2 + x ^ 2 = (8sqrt(3)) ^ 2 x ^ 2 + 8 ^ 2 = 12 ^ 2 sqrt(x ^ 2) = sqrt(80) x = 4sqrt(5) x ^ 2 + 64 = 144 sqrt(2.5 * 2) = 5sqrt(2) (sqrt(48))/(sqrt(16rho * 3)) = 4sqrt(3) (sqrt(19))/7 (14sqrt(2))/2 x ^ 2 + 1 ^ 2 = 2 ^ 2 sqrt^2 x = sqrt(3) x = sqrt(3) (v * 2)/(9 * 2) = 3sqrt(2) (12sqrt(3))/3 (9sqrt(10))/4 x ^ 2 = 8 ^ 2 + 6 ^ 2 x ^ 2 = 64 + 36 sqrt(x ^ 2) = sqrt(100) sqrt(100 * 40) = 10sqrt(LD) 15 * (9sqrt(5))/(sqrt(2)) * (sqrt(2))/(sqrt(2)) (15sqrt(6))/3 sqrt(18) * sqrt(2) 10.3sqrt(2) * 3sqrt(6) 5sqrt(6) sqrt(14p * 5) 2. (15sqrt(2))/(sqrt(3)) * (sqrt(3))/(sqrt(3)) 8sqrt(3) 4sqrt(3) 48sqrt(3) 24sqrt(4 * 3) = 13. 12/(sqrt(3)) * (sqrt(3))/(sqrt(3)) 14. 16/(sqrt(2)) * (sqrt(2))/(sqrt(2)) sqrt(2) 5. sqrt(600) ما 3 ^ 2 + 6 ^ 2 = x ^ 2 9 + 36 = x ^ 2 3sqrt(5) = x 45 = x ^ 2 16- C. Use the right triangles within other figures to set up and solve equations using the Pythagorean Theorem to find the value of x. rectangle I'SOS. A square 9. 6 10. 11. 3 15 4/2 12. T NEM equilat. A 2sqrt(3) 1 2sqrt(3) X 8 ^ 2 + 15 ^ 2 = x ^ 2 64 + 225 = x ^ 2 √289 17 = x x ^ 2 + x ^ 2 = (4sqrt(2)) ^ 2 5 2x ^ 2 = (4sqrt(2)) ^ 2 2x ^ 2 = 16 * 2 (2x)/2 = 32/2 2 3 + x ^ 2 = 4 * 3 3 + x ^ 2 = 12 (sqrt(3)) ^ 2 + x ^ 2 = (2sqrt(3)) x ^ 2 = 9 x = 3 x = 4 rhombus 13. + 14. 5 12 9 x ^ 2 + 12 ^ 2 = (4sqrt(13)) ^ 2 12 x ^ 2 + 144 = 16 * 13 x ^ 2 + 144 = 208 x ^ 2 = 64 225 = y ^ 2 15 = y : 1 + 144 = y ^ 2 9 ^ 2 + 12 ^ 2 = y ^ 2 4sqrt(3) 4sqrt(3) right trapezoid, rectangle attached. to 12 ^ 2 + (4sqrt(3)) ^ 2 = x ^ 2 144 + 16.3 = x 144 + 48 = x ^ 2 192 = x ^ 2 -> x = 8sqrt(3) D. Draw a diagram represent the figure and information provided in each problem. Then set up and solve an equation using the Pythagorean Theorem to find the requested value. 16. Find the length of the diagonal of a square with a perimeter of 14 54 4 14 14 ^ 2 + 14 ^ 2 = x ^ 2 14sqrt(2) 392 = x ^ 2 14 14 18. A vectangle has diagonals of 5 comod its widthiz sqrt(3) ) cm/ Find the length of the 17. The diagonals of a rhombus have lengths 18 and 24. Find the perimeter of the rhombus. X १ 9 ^ 2 + 12 ^ 2 = x ^ 2 2 81 + 144 =x-225 = x 15 = x 19. The perimeter of a rhombus is 100 cm, and one diagonal is 48 cm. Find the length the other diagonal. altitude 25 + 225 = x 5sqrt(10) = x 25 * 0 = x 17- 40-10-30 30/2 = 1S 5 ^ 2 + x ^ 2 = 15 ^ 2 25 x ^ 2 = 225 x = iota*v * sqrt(2) =aiti hvde x ^ 2 = 200 side-100-25 4 x ^ 2 + 24 ^ 2 = 25 ^ 2 x ^ 2 + 576 = 625 x = 7 x = 49 25 IS IS 25 24 X leg 10 x^ 15 ^ 2 + 15 ^ 2 - x ^ 2 x ^ 2 = 16 2sqrt(3) 12 + 4sqrt(13) 2 * zeta 2 \le Geometry/Trig 8.5 to 8.6 Practice 2 Name: Date: rections: 1. Label the side with OPP, ADJ, and HYP based on the angle you are trying to find. 2. Use the side you KNOW to determine the trig ratio to use. 3. Set up the equation and solve. Round answers to the nearest tenth. 1. 2. 3. H H H 27 0 14 D K tan x = 27/38 21 29 38 A A tan x= i4 2a A x = 35.4 x = 23, 2 x = 25.8 5. H 39 6. 10 D H 27 A H_{42} X = 72.2 Sin x = 10/39 A Siri x = 11 27 A 7. 8. 9. H 8 12 A H 20 13 A A 24 H 0 sin x = 12/24 x = 30 x = 49.5 10. 12. H 0 14 A 51 4 x = 36.4 85 680 x = 53.1 A A 48 50 H H x =14.c1 x = 41.4 sin x = 14/50 x = 24 cos x = 4/5 x = 16.3 tan x = (6gamma)/(5i) x = q/21 cos x = varphi/delta sin x = 40/42 11 0 cos x = 13/20