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:
it depends on what he means
Step-by-step explanation:
The friend needs to clarify the meaning of "if three lines intersect each other." If Line A intersects lines B and C, there will be two points of intersection, one at line B and one at line C.
If those lines are all in the same plane, and B and C are not parallel, so that line B intersects line C, then there will be a total of three points of intersection.
If the point of intersection of B and C is also the point where line A intersects them, then there will be only one point of intersection.
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So, if the meaning is "if there are three non-parallel lines in the same plane, and each intersects the other two", then the Line Intersection Postulate guarantees there will be 1 or 3 points of intersection.
If the meaning is "if there are three lines not necessarily in the same plane, and one intersects the other two (but those two don't intersect each other)", then there may be 1 or 2 points of intersection (allowing that all lines may intersect at the same point).
Let the total earnings be = x
Jennifer and Chris split the earnings in the ratio 3:2
Jennifer earned = $48


x=80
Hence total earnings are $80
(a) Chris earning is = 
Hence, Chris earns $32
(b) Jennifer spends 30% of her earnings on a book.
So, price of the book = 
Price of book = $14.40
(c) Jennifer also buys a magazine for = $5.40
So, total money Jennifer spent on book and magazine = 14.40+5.40=19.80
Money left with Jennifer = 48-19.80= $28.20
In fractions =
or multiplying the numerator and denominator by 10, we get
=
(d) Let the original price of the shirt = x
reduction percentage on x= 40%
Price paid after reduction = 16.80



Hence, the original price of the shirt was $42.
7 gallons for minute because 49 divided by 7 (which is the mins) would be 7. Leading to the answer of ) gallons per minute
Answer:
make it make sense then could answer