construct a∆ PQR in which PQ=8cm,angle 60degree,mediun RG from R to PQ is 5.8 cm.find the length of the altitude from R
toPQ
Answers
Answer:
this is the answer
Step-by-step explanation Required to construct: A triangle ABC,
Base AB = 5cm Median CM to the base = 4cm & vertical angle <C = 60°
Steps: 1: Draw a ray & cut segment AB = 5 cm
2: Construct BAD = 60° at point A on AB.
3: At A on AD , construct a perpendicular.
4: Now, draw perpedicular bisector of AB, which intersects the perpendicular of previous step at O
5: Taking O as centre & OA radius, draw a circle. This circle passes through A& B. And AD will be the tangent to this circle. Because radius OA is perpendicular to AD.
6 : M as centre, & 4 cm radius draw an arc, which cuts the arc of major segment at C
7: Join A,C & B,C.
ABC is the required triangle..
Justification: < DAB = 60° , which is formed by chord AB & tangent AD to the circle,
=> <DAB = < ACB = 60°. ( by alternate segment theorem, which states that angle formed by a tangent to the chord = angle formed by the chord at the alternate segment of the circle. And here we have constructed median AM = 4cm & AB = 5 cm..
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Hungenahalli Sitaramarao Badarinath
Hungenahalli Sitaramarao Badarinath, Ph.D. in Civil Engineering. Maths keeps one mentally active.
Answered May 17, 2017 · Author has 21.1k answers and 9.2m answer views
How do i construct a triangle with a base, median on the base and vertical angle?
Suppose you are required to construct a triangle with a base, BC (8 cm), median on the base, AD (12 cm) and vertical angle, <A (20 degrees).
Draw line BC of 8 cm length. So the base is ready. Mark the midpoint of BC and name it as D. The location of the median on the base is identified.
Next(180 - 2*20 = 140 and 140/2 = 70.)
At the two ends B and C make angles of 70 degrees to intersect at O. Angle BOC = 40 degrees.
With O as center and OB as radius draw a circle. BC will thus be a chord of the circle with center O.
With D as center and a radius of 12 cm intersect the major segment of the circle at A and A’. Now the median AD or A’D = 12 cm is located.
Join B to A and C to A. Now ABC is the desired triangle. <A = 20 degrees (half the angle subtended by the chord at the center of the circle). DA, the median = 12 cm. BC, the base = 8 cm. A’BC is another triangle with the same properties as ABC. So you have constructed the triangle you set out to draw!
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Shambhu Bhat
Shambhu Bhat, Retired professor in engineering ;Very fond of mathematics
Updated Jul 13, 2018 · Author has 2.1k answers and 995.8k answer views
I understand in △ABC,∠A,base BC, and median,AD are given.
Draw a line segment of length BC.
draw a⊥ ar bisector of BC.Draw a line from B making angle 90-A with BC to intersect the bisector drawn at O.
Draw a circle with center O and radius OB.
From midpoint of BC, D an arc of length=median to intersect the circle at A.
join AB and AC.
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