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Date Name Per. REVIEW Chapter 8: Trigonometric Ratios 8.1 Geometric Mean 1. Write a similarity statement comparing the three triangles in the diagram. 2. Find x, y, and z. z= J r i ^ z 7 3 n , 2 ^ if x= y= 5 7= 3. The Coast Guard has sent a rescue helicopter to retrieve passengers off a disabled ship. The ship has called in its position as 1.7 miles from shore. When the helicopter passes over a buoy that is known to be 1.3 miles from shore, the angle formed by the shore, the helicopter, and the disabled ship is 90°. Determine what t h ^ ^ i m e t e f w o u l d read to the nearest foot when the helicopter is directly above the buoy. ^ ^ 5 , ^ ^ ^ ^ aJhti^^^-c^ 52^6 ' '>^^ Name Per. Date 8.2 Trigonometric Ratios (Check that your calculator is in DEGREE mode. Tip: If tan45=l, then your calculator is in the correct mode.) 4. Trig Ratios: Soh-Cah-Toh s i n Z A : lf£i£l_ cosZA=''f^ t a n Z A = ^ ^ 5. Given the triangle below, find the sin, cos, and tan for angle M and T. As a fraction and decimal to the hundredths place. i—, R cos tin Z M = 1 ^ «-71 tail 6. If 0 = 14 ° and the hypotenuse is 12, what is the approximate perimeter of the triangle? a.) 14.5 26.5 c. ) 2.9 d. ) U.6 ^' ^ 1-2. ______ opp I -i, a^.--'=f''^'''^ 7. If c = 50 and angle X is 65 degrees, what is the approximate area of the triangle? a. ) b. ) do: 352.23 402.45 423.22 478.77 ft.^ b i t Per. Date Name 8. A right triangle has an angle that measures 55°. The leg adjacent to this angle has a length of 43 cm. What is the length of the other leg of the triangle? Round to the nearest tenth. -•an 6S - -q^ 9. Right triangle ABC is gfaphed on the coordinate plane and has vertices at A ( - l , 3), li(0, 5), and C(4, 3). What is the measure of Z C to the nearest^egre£2 8.3 Inverse of Trig. Ratios 10. Using trig ratios, Solve the right triangles. Round angles to the nearest degree and sides to the hundredths. a. /O CDS P S C0S3S d. 11. A ramp was built by the loading dock. The height of the loading platform is 4 feet. Determine the length of the ramp if it makes a 32° angle with the ground. 12. Janelle sets her treadmill grade to 6%. What is the angle that the treadmill surface makes with a horizontal line? Round to the nearest degree. A,^^ 13. If cos A= 0.28, which angle in the triangles below is Z A ? ^ ^ ^ ^ ^ ^ 9 cm 40 cm Name Date Per. 8.4 Angle of Elevation and Depression 14. A jet rises vertically 2000 feet over a horizontal distance of 2856 feet. To the nearest degree, what is the angle of elevation of the jet's path? 15. Mayuko is sitting 30 feet high in a football stadium. The angle of depression to the center of the field is 14°. What is the horizontal distance between Mayuko and the center of the field? Round to the nearest foot. I -^JH' -u«.^izj*_ 5 o So 4^nlM 16. A surveyor 50 meters from th^asejof a cliff measures the angle of elevation to the top of the cliff as 72°. What is the height of the cliff? Round to the nearest meter. X ^ So •^K>7P 4 yy-Or^hji. 17. The figure shows a person parasailing. What is x, the height of the parasailer, to the nearest foot? 3L? - > 18. Shane is 61 feet high on a ride at an amusement park. The angle of depression to the park entrance is 42°, and the angle of depression to his friends standing below is 80°. How far from the entrance are his friends standing? Round to the nearest foot. 19. Solve the following quadratic equations. a. 6 - 2 x 2 = -194 x - O ' b. - 5 + 4x2 = 11 20. Simplify the radicals a. VT25 b. VT92 - 5vr^ r gvTl ;i ^ -7. 4-4 j SmCi i t 5 t 4- r—r J r -4- ;—r-