In a Ale ABC, if the median and altitude drawn from vertex A, trisect angle A, then tan
B -|Cis
equal to
Answers
Given : ΔABC, if the median and altitude drawn from vertex A, trisect angle A,
To Find : tan | B - C |
Solution:
Let say AD ⊥ BC & AM is median
=> BM = CM = BC/2
Let say D lies between B & M
∠BAD = ∠DAM = ∠MAC = α and ∠A = 3α
in Δ ABD & Δ AMD
∠BAD = ∠DAM = α
AD = AD ( common)
∠ADB = ∠ADM = 90°
=> BD = DM
BD = DM = BM/2
=> DM = CM/2 ( ∵ BM = CM)
in ΔADC
∠DAM = ∠MAC = α hence AM is angle bisector
=> AD/AC = DM/CM
=> AD/AC = 1/2
ADC is right angled triangle
Hence CosC = AD/AC = 1/2
=> ∠C = 30°
∠DAC = 60°
∠DAC = ∠DAM + ∠MAC = 2α
=> α =30°
∠A = 3α = 90°
=> ∠B = 60°
tan | B - C | = Tan | 60° - 30° | = Tan 30° = 1/√3
if D would have been between M & C
then ∠B = 30° and ∠C = 60°
then tan | B - C | = Tan | - 30° | = Tan 30° = 1/√3
Learn More:
the given figure P and Q trisect the line segment bc of triangle ABC ...
https://brainly.in/question/3713079
P and Q are the points of trisection of the diagonal BD of a ...
https://brainly.in/question/5946948
Triangle ABC is a right angled triangle with angle B =90 degree D ...
https://brainly.in/question/13231423