Answer B
Step-by-step explanation:
I took the test and got it right
Answer:
0.01533036946190
Step-by-step explanation:
10÷652.3
0.01533036946190
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:
900,000
Step-by-step explanation:
I'm not sure how to explain rounding, but this should be the answer if ur asking for rounding to the nearest hundred thousand and not the hundredth thousand
9514 1404 393
Answer:
- 13 ft
- (a) 1 second; (b) t = 0, t = 1/2
Step-by-step explanation:
<h3>1. </h3>
Let w represent the length of the wire. Then the height of attachment is (w-1). The Pythagorean theorem tells us a relevant relation is ...
5² +(w -1)² = w²
w² -2w +26 = w² . . . . . . . eliminate parentheses, collect terms
26 = 2w . . . . . . . . . . . . add 2w
13 = w . . . . . . . . . . . . divide by 2
The length of the wire is 13 feet.
__
<h3>2. </h3>
(a) When h = 0, the equation is ...
0 = -16t^2 +8t +8
Dividing by -8 puts this into standard form:
2t^2 -t -1 = 0
Factoring, we get ...
(2t +1)(t -1) = 0
The positive value of t that makes a factor zero is t = 1.
It will take 1 second for the gymnast to reach the ground.
__
(b) When h = 8, the equation is ...
8 = -16t^2 +8t +8
Subtract 8 and divide by 8 to get ...
0 = -2t^2 +t
0 = t(1 -2t) . . . . factor out t
Values of t that make the factors zero are ...
t = 0
t = 1/2
The gymnast will be 8 feet above the ground at the start of the dismount, and 1/2 second later.
