Inaccessible 82710

Determine the distance between two inaccessible places K, L, if the angles KAL=62°10", LAB=41°23", KBL=66°34", and LBA were measured from points A, B, which are 870 m apart = 34°52".
Thank you.

Correct answer:

x =  749.853 m

Step-by-step explanation:

AB=870 m LBA=34°52=34°+6052°=34.8667°34.8667 LAB=21°23=21°+6023°=21.3833°21.3833  KAB=52°40=52°+6040°=52.6667°52.6667 KBA=81°15=81°+6015°=81.25°=81.25  ALB=180LABLBA=18060128315523=4495=123.75  AKB=180KBAKAB=18043253158=1255346.0833   LA:AB = sin LBA: sin ALB  LA=AB sinALBsinLBA=AB sin123.75° sin34.866666666667° =870 sin123.75° sin34.866666666667° =870 0.831470.571669=598.15982 m  KB=AB sinAKBsinKAB=AB sin46.083333333333° sin52.666666666667° =870 sin46.083333333333° sin52.666666666667° =870 0.7203490.795121=960.30498 m  LB=AB sinALBsinLAB=AB sin123.75° sin21.383333333333° =870 sin123.75° sin21.383333333333° =870 0.831470.364606=381.50181 m  KA=AB sinAKBsinKBA=AB sin46.083333333333° sin81.25° =870 sin46.083333333333° sin81.25° =870 0.7203490.988362=1193.69092 m  LAK=LABKAB=6012833158=601283603160=6012833160=601877=60187731.2833  LBK=KBALBA=432515523=604875602092=6048752092=60278346.3833   x2 = LA2 + KA2  2 LA KA cos LAK  x=LA2+KA22 LA KA cosLAK=LA2+KA22 LA KA cos(31.283333333334)° =598.15982+1193.690922 598.1598 1193.6909 cos(31.283333333334)° =598.15982+1193.690922 598.1598 1193.6909 0.85461=749.853=749.853 m



Did you find an error or inaccuracy? Feel free to write us. Thank you!







Tips for related online calculators
Need help calculating sum, simplifying, or multiplying fractions? Try our fraction calculator.
The Pythagorean theorem is the base for the right triangle calculator.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Related math problems and questions: