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2006-11-16 21:14:50 · 5 answers · asked by cartman 2 in Science & Mathematics ➔ Mathematics
a. Length of AC = 8 cm
b. to find length of CE
(AE)^2 = (AC)^2 + (CE)^2 (Pythagoras theorem)
10^2 = 8^2 + CE^2
100= 64 + CE^2
CE^2 = 100 – 64
CE = under root of (36)
CE = 6 cm
c. to find length of DB
sin 40 = 6/DB
DB = 6/sin40
DB = 6/0.64
Db = 9.38 cm
d. DE = DC + CE
for DC
tan40 = 6/DC
DC = 6/tan40
DC = 6/0.84
DC = 7.14 cm
Now DE = 7.14 + 6
DE = 13.14 cm
2006-11-16 21:34:46 · answer #1 · answered by burhanmz 2 · 0⤊ 0⤋
AC = 8 cm
CE = 6 cm
DB = 6/sin40 ≈ 9.33 cm
DE = 6 + 6/tan40 ≈ 13.15 cm
The triangle on the right is drawn approximately to scale. The one on the left is not.
2006-11-16 21:35:50 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋
a) Find the length of AC
AC = AB + BC
AC = 2 + 6
AC = 8 cm
b) Find the length of CE
To find CE we use pythagoras Theorem focusing only on triangle ACE we have that:
AE^2 = AC^2 + CE^2
making CE the subject of the formula we have that
CE^2 = AE^2 - AC^2
CE = sq rt (AE^2 - AC^2)
CE = sq rt (10^2 - 8^2)
CE = sq rt (100 - 64)
CE = sq rt (36)
CE = 6 cm
c) Find the length of DB
To find the length of DB, we focus only on triangle BCD.
Using SOHCAHTOA: Sine = Opposite/Hypotenus, Cosine = Adjacent/Hypotenus, Tangent = Opposite/Adjacent
We find that the Sine = Opposite/Hypotenus best suits our problem because we have the opposite side BC, we have an angle 40 degrees and we have one unknown side DB.
So:
Sin 40 = BC/DB
Sin 40 = 6/DB
DB = 6/Sin 40
DB = 6/0.643
DB = 9.33 cm
d) Find the total length of DE
To find DE, we first of all find DC and add it to CE.
To find DC, we focus on triangle BCD
Using Pythagoras Theorem again we have
DB^2 = BC^2 + DC^2
9.33^2 = 6^2 + DC^2
DC^2 = 9.33^2 - 6^2
DC = sq rt (9.33^2 - 6^2)
DC = sq rt (87.0489 - 36)
DC = sq rt (51.0489)
DC = 7.14 cm
DE = DC + CE
DE = 7.14 + 6
DE = 13.14 cm
2006-11-16 21:57:53 · answer #3 · answered by Loral 2 · 0⤊ 0⤋
i don't be conscious of what you advise with the help of a sum. Sum is the answer to an addition undertaking. to locate tan 38.2, use a calculator, press the tan button, then enter 38.2 and then press enter (=) to get the respond. Oh, be certain the calculator is in degree mode.
2016-12-29 03:45:51 · answer #4 · answered by ? 3 · 0⤊ 0⤋
a. AC = AB+BC = 2+6 = 8
b. According to pythagoras theorem (AC)^2 + (CE)^2 = (CE)^2
(8)^2 + (CE)^2 = (10)^2
64 + (CE)^2 = 100
(CE)^2 = 100-64
(CE)^2 = 36
(CE) = sqrt(36)
(CE) = 6
c. and d. sorry dont have much time.
2006-11-16 22:29:16 · answer #5 · answered by Paritosh Vasava 3 · 0⤊ 0⤋