EXAMPLES. XI.

1. Given a=254, B=16o, C=64°: find b.

3. Given a=1000, B=104o, C=24° 29′ 20′′: find b.

5. Given b=21, c=10.5, A=36° 52′ 12′′: find B and C.

=

=

log 2 3010300, L cot 18° 26' 6" 10.4771213. log 15-11760913,

6. Given b=426, c=354, A=49° 16′: find B and C. log 78=1.8920946,

log 72=1.8573325,

7. Given b=100, c=60,
log 2 3010300,

L cot 24° 38'

10'3386231,

Z tan 11° 22′ = 9.3032609,
L tan 11° 23' 9.3039143.

L cot 21° 15' = 10'4101858,

=

A=42° 30′: find B and C.

Z tan 32° 44' = 9.8080829,
Z tan 32° 45'9'8083606.

8. Given b=82471, c=63529, A=43° 10': find B and C.

log 18942=42774258,

log 146=21643529,

= 10'4027530,

Z tan 68° 25'
L tan 18° 9′ 20′′= 9.5157731,

Z tan 18° 9' 30" 9.5158442.

9. Given b=375400·1, c=3277629, A=57° 53′ 16′′8:

10. Given b=5·75, c=45, A=48° 20′: find B, C,

and a.

log 1.25 log 4.3485

=

log 4.5

=

log 10-2510107239,

L sin 50° 37′ 44′′ =
= 9.8882095.

11. Given a=528, b=252, A=124° 34': find B

and C.

13. Given a=21217, b=12'543, A=29° 51': find B

and C.

log 21217=4.3266840, log 12543=40984014,

L sin 17° 6′ 40′′ = 9'4686806,
L sin 170 6′ 50 =94687490,
L sin 29° 51' =9'6969947.

14. Given log a='
=9717973, log b='8929345,

A=70° 12′ 10′′: find B, C, and log c.

I sin 70° 12′ 10′′=9.9735422, L sin 58o 6′ 30′′=9′9289325.

L sin 51° 41' 20"-9.8946794,

15. Given a 36, b=44, A=32° 42': find B and C.

17. Given a = 222, b=318, c=406: find A.

18. Given a=11, b=13, c=16: find all the angles.

log 2=3010300,
log 3=4771213,
log 7='8450980,

L cot 21° 31'=10'4042321,
L cot 21° 32′ = 10'4038620,
L cot 41° 35'=10'0519190,

L cot 41° 36′100516645.

19. Given a=25, b=26, c=27: find all the angles.

20. If the angles of a plane triangle be in Arithmetical Progression, and the greatest side be to the least as 5 is to 4, find all the angles.

log 3=4771213,

I tan 10° 53′ 30′′=9.2842475,

L tan 10° 53' 40" 9.2843610.

XII. Heights and Distances.

114. We have already in Arts. 38...45 considered some of the cases which properly belong to the present Chapter; and the student is advised to read those Articles again before proceeding to the additional investigations which we shall now give.

115. To find the height of an inaccessible object placed on a hill.

Let P be the top of the object, PQ its height; let A and B be two points in a horizontal plane, such that P, Q, A, B are all in the same vertical plane. Let PQ produced meet BA produced at C. At 4 observe the angles PAC and QAC; at B observe the angle PBC; and measure AB.

The angle APB=PAC-PBC, and is therefore known.

The angle PAQ=PAC-QAC, and is therefore known. The angle PQA=QCA+QAC=90°+QAC, and is therefore known.