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Construction of a Right Triangle Whose One Side and Hypotenuse Are Given

Which vertex ...

Question

Which vertex of $Δ$ ABC is right angled if $¯ ¯¯¯¯¯¯ ¯ A B$ = 8 cm, $¯ ¯¯¯¯¯¯ ¯ A C$ = 6 cm, and $¯ ¯¯¯¯¯¯ ¯ B C$ = 10 cm?

A

∠ C

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B

∠ A

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C

∠ B

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D

A o r C

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Solution

The correct option is B $∠ A$
From the given measurements, $¯ ¯¯¯¯¯¯ ¯ B C$ is the hypotenuse. The angle opposite to $¯ ¯¯¯¯¯¯ ¯ B C$ is $∠ A$ which is a right angle.

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Similar questions

∆ A B C, A D

is the bisector or

∠ A .

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.
(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.
(iii) If AB = 5.6 cm, BD = 3.8 cm and BC = 6 cm, find AC.
(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

Q. In Fig. 4.60, check whether AD is the bisector of ∠A of ∆ABC in each of the following:

(i) AB = 5 cm, AC = 10 cm, BD = 1.5 cm and CD = 3.5 cm
(ii) AB = 4 cm, AC = 6 cm, BD = 1.6 cm and CD = 2.4 cm
(iii) AB = 8 cm, AC = 24 cm, BD = 6 cm and BC = 24 cm
(iv) AB = 6 cm, AC = 8 cm, BD = 1.5 cm and CD = 2 cm
(v) AB = 5 cm, AC = 12 cm, BD = 2.5 cm and BC = 9 cm

Q. If a ∆ ABC, AD is the bisector of ∠A, meeting side BC at D.

(i) If BD = 2.5 cm, AB = 5 cm and AC = 4.2 cm, find DC.
(ii) If BD = 2 cm, AB = 5 cm and DC = 3 cm, find AC.
(iii) If AB = 3.5 cm, AC = 4.2 cm and DC = 2.8 cm, find BD.
(iv) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.
(v) If AC = 4.2 cm, DC = 6 cm and BC = 10 cm. find AB.
(vi) If AB = 5.6 cm, AC = 6 cm and DC = 3 cm, find BC.
(vii) If AD = 5.6 cm, BC = 6 cm and BD = 3.2 cm, find AC.
(viii) If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC.

In a $Δ A B C$ , AD is the bisector of $∠ A$ .

(i) If AB = 6.4 cm, AC = 8 cm and BD = 5.6 cm, find DC.

(ii) If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.

(iii) If AB = 5.6 cm, BD = 3.2 cm and BC = 6 cm, find AC.

(iv) If AB = 5.6 cm, AC = 4 cm and DC = 3 cm, find BC.

Δ A B C

A D

is the bisector of

∠ B A C

A B = 10 c m, A C = 14 c m

B C = 6 c m

B D

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