Lesson 32: Using Trigonometry to Find Side Lengths of an Acute Triangle

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1 : Using Trigonometry to Find Side Lengths of n Aute Tringle Clsswork Opening Exerise. Find the lengths of d nd e.. Find the lengths of x nd y. How is this different from prt ()? Exmple 1 A surveyor needs to determine the distne etween two points A nd B tht lie on opposite nks of river. A point C is hosen 160 meters from point A, on the sme side of the river s A. The mesures of ngles BAC nd ACB re 41 nd 55, respetively. Approximte the distne from A to B to the nerest meter. : Using Trigonometry to Find Side Lengths of n Aute Tringle Dte: 10/28/14 S.201 This work is liensed under

2 Exerises In ABC, m A 30, 12, nd 10. Find sin B. Inlude digrm in your nswer. 2. A r is moving towrds tunnel rved out of the se of hill. As the ompnying digrm shows, the top of the hill, H, is sighted from two lotions, A nd B. The distne etween A nd B is 250 ft. Wht is the height, h, of the hill to the nerest foot? Exmple 2 Our friend the surveyor from Exmple 1 is doing some further work. He hs lredy found the distne etween points A nd B (from Exmple 1). Now he wnts to lote point D tht is equidistnt from oth A nd B nd on the sme side of the river s A. He hs his ssistnt mrk the point D so tht the ngles ABD nd BAD oth mesure 75. Wht is the distne etween D nd A to the nerest meter? : Using Trigonometry to Find Side Lengths of n Aute Tringle Dte: 10/28/14 S.202 This work is liensed under

3 Exerise 3 3. Prllelogrm ABCD hs sides of lengths 44 mm nd 26 mm, nd one of the ngles hs mesure of 100. Approximte the length of digonl AC to the nerest mm. : Using Trigonometry to Find Side Lengths of n Aute Tringle Dte: 10/28/14 S.203 This work is liensed under

4 Prolem Set 1. Given ABC, AB 14, A 57.2, nd C 78.4, lulte the mesure of ngle B to the nerest tenth of degree, nd use the Lw of Sines to find the lengths of AC nd BC to the nerest tenth. Clulte the re of ABC to the nerest squre unit. 2. Given DEF, F 39, nd EF 13, lulte the mesure of E, nd use the Lw of Sines to find the lengths of DF nd DE to the nerest hundredth. 3. Does the lw of sines pply to right tringle? Bsed on ABC, the following rtios were set up ording to the lw of sines. Fill in the prtilly ompleted work elow. Wht onlusions n we drw? : Using Trigonometry to Find Side Lengths of n Aute Tringle Dte: 10/28/14 S.204 This work is liensed under

5 4. Given qudrilterl GHKJ, H 50, HKG 80, KGJ 50, J is right ngle nd GH 9 in., use the lw of sines to find the length of GK, nd then find the lengths of GJ nd JK to the nerest tenth of n inh. 5. Given tringle LMN, LM 10, LN 15, nd L 38, use the lw of osines to find the length of MN to the nerest tenth. 6. Given tringle ABC, AC 6, AB 8, nd A 78. Drw digrm of tringle ABC, nd use the lw of osines to find the length of BC. Clulte the re of tringle ABC. : Using Trigonometry to Find Side Lengths of n Aute Tringle Dte: 10/28/14 S.205 This work is liensed under

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