in trangle ADB , angle D is 30 and angle B is 45 If AC with length 25 is drawn perpendicular from A onto to BD which is point C , what is the length of BD ?
2007-11-16 03:55:34 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
ADC = 30 side opposite to 30 is half of hypotenuse. so Hypotenuse AD = 50
angle DAC = 60 angle side opposite to 60 is rt3/2 times hypotenuse.
DC = (rt3/2) × 50 = 25 rt3
angle ABC = 45 so angle BAC = 45 so AC = CB = 25
DB = DC + CB = 25 rt3 + 25 = 25 (1 + rt3)
=25(2.732) = 68.3 units
2007-11-16 04:27:15 · answer #1 · answered by Pranil 7 · 0⤊ 0⤋
In triangle ABD
m
m
AC = 25 (given)
Now in triangle ABC
m
m
so m
tan CAB = BC/AC
tan(45) = BC/25
BC = 25 tan(45) = 25
In triangle ACD
m
m
m
tan(CAD) = CD/AC
tan(60) = CD/25
CD = 25(tan60) = 25 sqrt(3)
BD = BC + CD = 25 + 25sqrt(3)
BD = 25(1 + sqrt(3)) = 25(2.732)
BD = 68.3 units
2007-11-16 12:17:43 · answer #2 · answered by mohanrao d 7 · 0⤊ 0⤋
length BC is 25, length CD is 25(square root 3). Length BD is 25 + 25(square root 3).
2007-11-16 12:08:11 · answer #3 · answered by John & Vickie S 1 · 0⤊ 0⤋
triangle ADC is a 30-60-90 dehree triangleIts short leg = 25. So its long leg = CD = 25sqrt(3)
2007-11-16 12:03:54 · answer #4 · answered by ironduke8159 7 · 0⤊ 1⤋
tan(30)=25/ DC
DC=25/tan(30)
tan(30)=0.5775
DC=43.39
tan(45)=1
BC=25/tan(45)=25
BD=DC+BC=43.39+25=68.39
2007-11-16 12:16:14 · answer #5 · answered by cidyah 7 · 0⤊ 0⤋
draw it to scale.. it will help :)
2007-11-16 12:03:35 · answer #6 · answered by <3 3 · 0⤊ 0⤋