In the triangle ACE, CD is the perpendicular dropped from C to AE. The angle CAD is bisected by AB.
Given: DAB = CAB = 10 Deg, BCE = 40 Deg.
Question: What's the angle marked θ ? (angle BED)
aaa einsteinCAD
tan 20 = CD/AD --- 1
BAD
tan 10 = BD/AD --- 2
1/2
tan 20/tan 10 = CD/AD / BD/AD
tan 20/tan 10 = CD/BD --- X
ACD = 180 - (90 + CAD) = 180 - (90+20) = 70
AEC = 180 - (20 + ACE) = 180 - (20+70+40) = 50
CED
tan 50 = CD/DE --- 3
BED
tan a = BD/DE --- 4
3/4
tan 50/ tan a = CD/DE / BD/DE
tan 50/ tan a = CD/BD --- Y
X = Y
tan 20/tan 10 = tan 50/ tan a
tan a = tan 50 * tan 10 / tan 20
a = arctan (tan 50 * tan 10 / tan 20)
a =හරියට මතක නෑ
tan from rapidtables.com
a = arctan (1.19175359 * 0.17632698 / 0.36397023)
a = arctan (0.5773502723804037)
arctan from math.net
a = 30.000000137°
This is correct .. exactly what my son provided as the solution. I asked him to simplify this further, he just said you do.. use Mathematica or something.CAD
tan 20 = CD/AD --- 1
BAD
tan 10 = BD/AD --- 2
1/2
tan 20/tan 10 = CD/AD / BD/AD
tan 20/tan 10 = CD/BD --- X
ACD = 180 - (90 + CAD) = 180 - (90+20) = 70
AEC = 180 - (20 + ACE) = 180 - (20+70+40) = 50
CED
tan 50 = CD/DE --- 3
BED
tan a = BD/DE --- 4
3/4
tan 50/ tan a = CD/DE / BD/DE
tan 50/ tan a = CD/BD --- Y
X = Y
tan 20/tan 10 = tan 50/ tan a
tan a = tan 50 * tan 10 / tan 20
a = arctan (tan 50 * tan 10 / tan 20)
a =හරියට මතක නෑ
tan from rapidtables.com
a = arctan (1.19175359 * 0.17632698 / 0.36397023)
a = arctan (0.5773502723804037)
arctan from math.net
a = 30.000000137°
ඕක තමයි මටත් ආවේ . simplify කරන්න බැලුව හරිගියේ නෑ . ගැහුවා cal එකේ 30 ආව .This is correct .. exactly what my son provided as the solution. I asked him to simplify this further, he just said you do.. use Mathematica or something.
Can anyone simplify Tan^-1 (Tan 50 * Tan 10)/ Tan20 ?
අහ් මේක දැක්කෙ දැනුයි@AnuradhaRa අනුරාධ රාමානුජන්
අනේ පලයන් උබට හොඳට maths පුලුවන්. dilan, sanjeewakaru, DHE ඔය ඔක්කොම එකතු කරහම එන දැනුමට වඩා දැනුමක් උඹට තියෙනවා. උඹට උඹවම විස්වාස නෑ. ඒකයි වැරැද්ද.
Ai Candid-bඅනේ පලයන් උබට හොඳට maths පුලුවන්. dilan, sanjeewakaru, DHE ඔය ඔක්කොම එකතු කරහම එන දැනුමට වඩා දැනුමක් උඹට තියෙනවා. උඹට උඹවම විස්වාස නෑ. ඒකයි වැරැද්ද.
මායි උඹයි එක මට්ටමේ වගෙ ඉන්නවඅනේ පලයන් උබට හොඳට maths පුලුවන්. dilan, sanjeewakaru, DHE ඔය ඔක්කොම එකතු කරහම එන දැනුමට වඩා දැනුමක් උඹට තියෙනවා. උඹට උඹවම විස්වාස නෑ. ඒකයි වැරැද්ද.
මට හදාගන්න බැරුව ගියාCan anyone simplify Tan^-1 (Tan 50 * Tan 10)/ Tan20 ?
Since nobody answered this is the solution. So the inverse tan of the expression is exactly 30 degrees. @dilann please note.
(Equations entered using iMathEQ)
nice one.Can anyone simplify Tan^-1 (Tan 50 * Tan 10)/ Tan20 ?
Since nobody answered this is the solution. So the inverse tan of the expression is exactly 30 degrees. @dilann please note.
(Equations entered using iMathEQ)
