Question

1.5.58 J Balloon A hot air balloon is between two spotters who are 1.6 miles apart. One spotter reports that the angle of elevation is 69º and the other reports that it is 74°. What is the altitude of the balloon? ked miles (Round to one decimal place as needed.) scon omis

Answer 1

Que Criven distance b/w the spotters = 1.6 miles Angle of elevation of 1st spotter, let a = 69° | Angle of elevation of and spotten, let ß=74 sol. Let the 1st spotter be at point A, 2nd spotter be at point B and the balloon at point c, forming a triangle. Let CDI AB & CD = b 18274 h d=69 kaDelf-x het BD = x then AD= 1.6-x Now, in light D BDC- tan ß = CD - BD tan 74 = b x

- х = co Ь tan 74 In - right a CDA tan a = CDT AD tan 69° = b. » 1.6-x » 1.6-x= b tanog > x= 1.6- b tanogo compairing 0 & b = 1.6- b tan 74o tan 69° b + b = 1.6 tan 74 tan ogo bitan 69°+ b tantho=1:6 tantu tanogo b= 1.6 (tanthi tan69°) (stan 69°+ tan 74°)

>> b = 1.6 / 9.085025232) - 6.09 2503509 + b = 14.5360 4037 6:092503509 b = 2.38588 9536 [b ñ 2-4 of the balloon Hence, the altitude iu 2.4 miles.