Summary: p.28, 53,74,99 Key oncepts: Basic Trig Rations, osine Law, Sine Law, The Ambiguous ase Practice Questions p.54, 200 2S- ( ui A opposite. _7 x ri x,4 Example #2: Find the hypotenuse 3 éca- (c; s ()S3 sj.i( ).37 4 5 ft ; ;53 s; ( ) 37 To Find Angle A To Find Angle B Example: Find both angles using sine, cosine and tangent. sinx = hypotenuse adjecent adjacent cosx = hypotenuse tanx = opposite SOHAHTOA These ratios only apply to t I\ I Basic Trigonometry Ratios Textbook p.6-54, 62-200 hapter 3&4 Review: Trigonometry
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To determine which case you have, compare the second given side to the ii ( t two solutions. For triangles where you are given ASS. there maybe no solutions, one solution or The Ambiguous ase of the Sine Law (LI STEP #3 :(.2 q;,c- V STEP# OLi and another side 350 m long. The opposite angle to the 350 m side measures 20. Determine the length of the third side, to the nearest metre. Show your work. Key Example: A landowner says that his property is triangular, with one side 500 m long 0. v v7 H -t 29 2..ScLcI(OISJ) STEP #2 3ct-VE :v \ -e 3,2If \ (, LY 3 7,, ase # (no solution) ase #2 (one solution - right) )le: One angle is 30, and the next side is... HLY - L Si O of the triangle.
Practice #: Find the unknown length or angle for each triangle (x). 2cc rvuis elctk-. -,,-)_ K cs b L I2 is 200 meters. What is the distance from the pilot to the point on the ground? that is some distance away. The angle of depression is 28, and the plane s altitude Practice #3: The p4fio t of an airplane in flight looks down at a point on the ground -x c,, -, long is the ladder 7 ç the ground. The bottom of the ladder is 28 feet from the base of the building. How Practice #2: A fireman rests his ladder against a building, making a 57 angle with ),\ siio ( K-: x K 5.-i Y5 ii -,60 45.. 7 x 0,0 x IiZ 7 hapter 3&4 Review: Trigonometry L (
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#5: Solve each of the following triangles (ie. the triangle and label ALL of the unknown angles and lengths) ( Practice draw a) In a right triangle IXPQR, the hypotenuse, q, is 2 m long and length of sides p and r to the nearest tenth of a metre. b) ii LP = 25. Determine the ç L ( p fo In t.ab, LA = 65, a = 23.5 cm, and L= 7. Determine the le nearest of a centimetre. tnth \\) n c hfiiëc to the c) In AXYZ, LX 50, LY 80, and 4 cm,. Determine angle Z, to the nearest tenth of a degree. A ii A io ) 7 - Practice #6: For each description below possible triangles. a. In ADEF, d = 5cm, e 3cm, f = 9cm. determine if there 4ThO ) 4 LJ are ero, one, or two b.inaab, LA=25,b 3m,c=lOm. 4 c.inajijj =0.4km,k=.6km. d. In APQR, LP 7, LQ 0, r = 26mm. N > L Tc r. V S e. In AFTJN, LF = 75, f = 25cm, n = 47cm. A;5,LI Vb V 0 IV.,AJI (
Practice #8: Determine two angles between 0 and 80 that have the sine ratio 0.8480 c; (27_c 5i r - & 5E. How far apart are the boats after.5 hours? i vl :- 7 j AS :23 other makes a 55 angle with the ground. Draw a diagram of the situation. Then, determine the length of each wire to the nearest metre. the ends of the wire are 235 m apart. One wire makes a 75 angle with the ground. The Practice #: A radio tower is supported by two wires on opposite sides. On the ground, X2 \ 30 )( _(i) kmlh in the direction N3OW, and the other is going an average of 24 kmlh in the direction Practice #0: Two boats leave the dock at the same time. One is going an average of 30 5 X >-,Z 3c2.()c)sX the nearest inch. is 8 ft. Determine the angle through which the pendulum swings. Round your answer to long, and when the pendulum swings from side to side, the horiontal distance it travels Practice #9: At Science World, there is a giant pendulum on display. The line is 30 feet Il Practice #7: Write another sine ratio that is equivalent to sin 44.
V Practice #2: In a parallelogram, two adjacent sides measure 7 cm and 4 cm. The shorter diagonal is cm. Determine, to the nearest degree, the measures of the larger angles in the parallelogram. r- i5via 4 26 2D() i fi (7Z( ti-i?,í)(f)ôs x io. ç Practice #3: A canoeist leaves the dock and paddles toward a buoy 40 m away. reaching the buoy, she changes directions and paddles another 80 m. From the dock, the angle between the buoy and the canoeist s current position measures 25. How far is the canoeist from the dock? Give two possible answers. Show your work. - -? -- ii (L(Q I.2X flu) - - Th T.J rtknle c2 -. 22: th-,) TtF cct TtAJ 2- - Th.. Practice #4: A farmer finishes repal? atënce post and then walks 200 yd through his corn field. He turns and walks another 250 yd east, until he can see the fence post directly southwest of him. He realies that he left some of his tools at the fence post and heads directly back to it. How far does he need to walk, to the nearest metre? () t (A ):... Twc ottiov (?..). S S i5 i I YI 7 7 0 (, ar) E f7. ( ( -7:4.( 72 - $ I 2 iy,i I