Answered

IDNLearn.com is designed to help you find reliable answers to any question you have. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.

Isaac and Albert spot a hot air balloon flying at a low altitude. They decide to calculate its height by standing 400 feet apart on a level surface and measuring the angle of elevation to the balloon. From
Albert, the balloon was at an angle of elevation of 62°and from Issac its was 48º. Determine the height of
the balloon above the ground to the nearest foot.

Sagot :

Answer:

144 feet to nearest foot.

Step-by-step explanation:

Let the distance between Albert and the point on the ground that the balloon is directly above be x feet Then for Isaac the distance is 400 - x feet

So we have 2 right angled triangles and:

tan 62 = h/x

tan 48 = h / (400- x)         where h is the height of the balloon.

From the first equation x = h / tan 62 so plugging this into the second one:

tan 48 =  h /  ( 400 - h/tan 62)

h = 400 tan 48 - h tan 48 tan 62

h + h tan 48 tan 62 = 400 tan 48

h ( 1 + tan48 tan62) = 400 tan48

h = 400 tan 48 / (1 +  tan 48 tan 62)

= 143.8 feet.

Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.