The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are 21° 19' and 16°20'.
1) Convert the angles to decimal form:
19' * 1°/60' = 0.32° => 21° 19' = 21.32°
20' * 1°/60' = 0.33° => 16° 20' = 16.33°
2) Deduce the trigonometric ratios from the verbal information.
You can form a triangle with
- horizontal leg x + 65 feet
- elevation angle 16.33°
- vertical leg height of the tree, h
=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)
You can form a second triangle with:
- horizontal leg x
- elevation angle 21.32°
- vertical leg height of the tree, h
=> trigonometric ratio: tan(21.32) = h / x => h = x * tan(21.32)
Now equal the two expressions for h:
(x+65)*tan(16.33) = x*tan(21.32)
=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet
=> h = 195.73 * tan(21.32) = 76.39 feet.
Answer: 76.39 feet
So this is what i did but im not sure if its 100% correct
585 / 9 to get the number of groups = 65
then you take 65 x 3 for number of students in each group and you get the final answer of 195 students
65-9=56
56 divided by 8 is 7
So they will need 7 tents
Try this option:
if x+y=-9 is I (one)
and x+2y=-25 is II (two), then
if II-I, then (x+2y)-(x+y)=-25+9 ⇔ y=-16.
Split the shape in 3 rectangles
4x2=8x2= 16 ( the bottom and top rectangle)
6x2= 12 (middle rectangle)
16+12=28
