Question

Find heighth in the picture below. Do parts (a) - (c). Х h a) Re-draw and label the picture on your paper. Find the interior angles for the small oblique triangle (one of its interior angles is 28 degrees) b) Use the Law of Sines to find x (exactly). c) Use right triangle trigonometry to find h Round your answer to three significant digits 38 440 ft

Answer 1

А Answer: (a) the small oblique triangle is ACD LACD + LACB [ supplementoy angles] h = 180° 38° D 440 ft » ZACD + 38° = 180° [ LACB = 380] ZACD 180°-38° = 148° ZACD or in A ADC , LC = 142° Now, in AADC LA + Lo + LC 180° 180 [ sum of interior angles of triangle is always 1800] ZA + 28° + 1420 LA + 170 = 180° ZA = 180°-170 LA 109 SO, small oblique the interior angles for angles for the triangle are : 1142, 10,28

Formula Used: law of sines! A c b Note: side a is opposite to angle a similarly side b is opposite to LB side c is opposite to angle c & C a B in A ABC law of sines state that sina sinB sinc - с. b

(6) in ДАDC. 28° LA = 10° LO 2 С = 142 CO = 440 have we by the law of sines, sin A sinc AD CD sin 10 sio 1489 x 440 xx sin10° = 440 x Sin 1420 multipli- [ Cross cation 440 x Si9142° Sinio 440 X 0.6156614 0:1736481 2 270.891016 0.1736481 x 1559.999 ftler is Answer

© ДАВО ADEX = 1559.999 in LD = 28° we know that, sino - side opposite to angle o Hypotenuse SO, sin (289) il xls x b 1559.999 = b = 1559.999 xsin (289) 2.1559.999 x 0.469471 or 732.3751 h = 732 ft is Answer