question_answer

 

Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

Assertion In a right angled triangle, if \[\tan \theta =\frac{3}{4}\], then greatest side of the triangle is 5 units.

Reason \[{{\left( greatest\text{ }side \right)}^{2}}={{\left( hypotenuse \right)}^{2}}\]

\[=\text{ }{{\left( perpendicular \right)}^{2}}+{{\left( base \right)}^{2}}\]

 

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is false.

D) A is false; R is true.

Correct Answer: A

Solution :

Assertion

Given,   \[\tan \theta =\frac{3}{4}\]

\[\tan \theta =\frac{p}{b}\]

Perpendicular = 3 units base = 4 units

Apply Pythagoras theorem,

\[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]

\[\Rightarrow \,\,\,A{{C}^{2}}={{3}^{2}}+{{4}^{2}}\]

\[\Rightarrow \,\,AC=\sqrt{9+16}=5\] units

Reason is true and correct explanation of the Assertion.