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In a triangle A B C , the altitude from ...

In a triangle `A B C ,` the altitude from `A` is not less than `B C` and the altitude from `B` is not less than `A C` . (a)The triangle is right angled (b) isosceles obtuse angled (d) equilateral

A

right angled

B

isosceles

C

obtuse angled

D

equilateral

Text Solution

Verified by Experts

The correct Answer is:
A
Given `c sin B ge a`
`rArr sin C sin B ge sin A`
and `a sin C ge b`
`rArr sin C sin A ge sin B`
`rArr sin C sin A ge sin B ge (sinA)/(sinC)`
`:. Sin^(2) C ge 1`
`rArr sin C = 1`
`rArr angle C " is " (pi)/(2)`
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CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercises
  1. In a triangle ABC, (a+b+c)(b+c-a)=kbc if

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  2. Let D be the middle point of the side B C of a triangle A B Cdot If th...

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  3. In a triangle A B C , the altitude from A is not less than B C and the...

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  4. In A B C , if (sinA)/(csinB)+(sinB)/c+(sinC)/b=c/(a b)+b/(a c)+a/(b c...

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  5. If in A B C , side a , b , c are in A.P. then B > 60^0 (b) B<60^0 B...

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  6. In a DeltaABC, AD is the altitude from A. Given b gt c, angleC=23^(@)"...

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  7. If the sides a , b , c of a triangle A B C form successive terms of G....

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  8. In triangle A B C ,b^2sin2C+c^2sin2B=2bc where b=20 ,c=21 , then i...

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  9. In a A B C ,ifA B=x , B C=x+1,/C=pi/3 , then the least integer value ...

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  10. If one side of a triangle is double the other, and the angles on opp...

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  11. If the hypotenuse of a right-angled triangle is four times the length ...

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  12. If P is a point on the altitude AD of the triangle ABC such the /C B P...

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  13. With usual notations, in triangle A B C ,acos(B-C)+bcos(C-A)+c"cos"(A-...

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  14. If 8R^2=a^2+b^2+c^2 then show that the triangle is right angled

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  15. Let ABC be a triangle with /A=45^0dot Let P be a point on side BC with...

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  16. In any triangle A B C ,(a^2+b^2+c^2)/(R^2) has the maximum value of 3 ...

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  17. In triangle A B C ,R(b+c)=asqrt(b c),w h e r eR is the circumradius of...

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  18. In A B C , if b^2+c^2=2a^2, then value of (cotA)/(cotB+cotC) is

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  19. If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 ...

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  20. If D is the mid-point of the side B C of triangle A B C and A D is per...

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