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
Answer: 96%
Step-by-step explanation:
There are 25 total cyclists and 24 of those finished the race in less than 51 minutes. The question would like this 24 to be expressed as a percentage of 25.
In percentage this would be:
= Number of cyclists who finished in 51 minutes / Total number of cyclists * 100%
= 24 / 25 * 100%
= 96%
Step-by-step explanation:
What do u mean by reflected on the axis? You want the equation?
Let x: the number of restaurants gift cards, and y: numbers of movie theaters gift card
50x+20y=450
x+y=15, so x=15-y
50(15-y)+20y=450
750-50y+20y=450
y=10
x=5.
As a result, Mr. Thompson buys 10 movie theaters give cards, and 5 restaurants gift cards. Hope it help!
