If three sides of a triangle are a-3 a and -2 a- then the measure of the angle opposite to the longest side is-

The sides form a pythagorian triplet because the sum of square of 2 sides ( a and √(2a)) is equal to the square of the third side (i.e. √(3a)) Thus, triangle is ...

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Standard IX

Mathematics

Pythagoras Theorem

If three side...

Question

If three sides of a triangle are a , $\sqrt{3}$ a and $\sqrt{2}$ a, then the measure of the angle opposite to the longest side is:

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Solution

The sides form a pythagorian triplet because the sum of square of 2 sides ( a and $\sqrt{2 a})$ is equal to the square of the third side (i.e. $\sqrt{3 a})$
Thus, triangle is a right angled triangle. This means the greatest angle is 90 degree.
We know that, in a triangle, the greatest angle lies opposite to the greatest side.
Thus, the angle opposite to greatest side will be 90 degrees

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Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

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(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.

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If three sides of a triangle are a , √3 a and √2 a, then the measure of the angle opposite to the longest side is:

If three sides of a triangle are a , $\sqrt{3}$ a and $\sqrt{2}$ a, then the measure of the angle opposite to the longest side is: