Q:

URGENT!! The diagram shown below represents the height of a blimp flying over a football stadium. Find the height of the blimp if the angle of elevation at the southern end zone, point A, is 70∘, the angle of elevation from the northern end zone, point B, is 62∘, and the distance between the viewing points of the two end zones is 145 yards. Round your answer to the nearest tenth and do not include units.

Accepted Solution

A:
Answer:The height of the blimp over the football stadium = 161.9 yardsStep-by-step explanation:* We will consider that the 3 points construct ΔABC- To find the height of the blimp over the football stadium,   draw CD perpendicular to AB and intersect it at D- CD is the height of the blimp over the football stadium* Now lets think how we will solve the problem- We have two right triangles ADC and BDC- The height CD is opposite to angle A of measure 70°  and to angle B of measure 62°∵ AD + DC = 145 yards- We can split them ⇒ let AD = x, then BD = 145 - x∴ AD = x , BD = 145 -x∵ tanФ = opposite/adjacent∴ tan(70) = CD/AD and tan(62) = CD/BD* Make CD as a subject using cross multiplication∴ CD = AD tan(70) and CD = BD tan(62)* Now we can equate them∴ AD tan(70) = BD tan(62)* Substitute AD and BD by their values∴ xtan(70) = (145 - x)tan(62) ⇒ open the bracket∴ xtan(70) = 145 tan(62) - xtan(62) ⇒ collect like terms∴ xtan(70) + xtan(62) = 145 tan(62) ⇒ take x as a common factor∴ x[tan(70) + tan(62)] = 145 tan(62) ⇒ divide 2 sides by [tan(70) + tan(62)] ∴ x = [145 tan(62)]/[tan(70) + tan(62)] = 58.922498∵ AD = x∴ AD = 58.922498* Use this value to find the height CD∵ CD = x tan(70)∴ CD = 58.922498 × tan(70) = 161.888234- Proximate the value to the nearest tenth∵ The hundredth digit is 9∴ Add the tenth digit by 1∴ CD = 161.9 ⇒ to the nearest tenth* The height of the blimp over the football stadium = 161.9 yards