1.3 puzzle time why did the fraction jump into boiling water
1 answer:
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Correct answer is: distance from D to AB is 6cm
Solution:-
Let us assume E is the altitude drawn from D to AB.
Given that m∠ACB=120° and ABC is isosceles which means
m∠ABC=m∠BAC =
And AC= BC
Let AC=BC=x
Then from ΔACD , cos(∠ACD) =
Since DCB is a straight line m∠ACD+m∠ACB =180
m∠ACD = 180-m∠ACB = 60
Hence
Now let us consider ΔBDE, sin(∠DBE) =
Note necessary facts about isosceles triangle ABC:
- The median CD drawn to the base AB is also an altitude to tha base in isosceles triangle (CD⊥AB). This gives you that triangles ACD and BCD are congruent right triangles with hypotenuses AC and BC, respectively.
- The legs AB and BC of isosceles triangle ABC are congruent, AC=BC.
- Angles at the base AB are congruent, m∠A=m∠B=30°.
1. Consider right triangle ACD. The adjacent angle to the leg AD is 30°, so the hypotenuse AC is twice the opposite leg CD to the angle A.
AC=2CD.
2. Consider right triangle BCD. The adjacent angle to the leg BD is 30°, so the hypotenuse BC is twice the opposite leg CD to the angle B.
BC=2CD.
3. Find the perimeters of triangles ACD, BCD and ABC:
4. If sum of the perimeters of △ACD and △BCD is 20 cm more than the perimeter of △ABC, then
5. Since AC=BC=2CD, then the legs AC and BC of isosceles triangles have length 20 cm.
Answer: 20 cm.