Question

65 points!!!!!!!!!

Malaya is standing directly between a 90 foot tall courthouse and a 54 foot tall bank. If the angle of elevation from the point where Malaya is standing to the top of the courthouse is 72 degrees, while the angle of elevation to the top of the bank is 35 degrees. What is the distance between the courthouse and the bank? Show all your work to get credit!

Answer 1

106.3ft

Explanation:

x= tan72=90/x

x= 90/tan 72

x= 29.2

y= tan35=54/y

y= 54/tan35

y= 77.1

x+y= answer

29.2 + 77.1 = 106.3

Answer 2

• 106.36 ft

Explanation:

Let the distance from the point Malaya is standing to the courthouse be x and the distance to the bank is y

• x + y is the distance between the courthouse and the bank

Then we have:

• x/90 = cot 72° ⇒ x = 90 cot 72° = 90*0.3249196962 = 29.24 ft (rounded)
• y/54 = cot 35° ⇒ y = 54 cot 35° = 54*1.4281480067 = 77.12 ft (rounded)
• x + y = 29.24 + 77.12 = 106.36 ft