Assertion (A): If the ratio of the height of a pole and its shadow is \sqrt3:1, then the Sun’s altitude is {30}^\circ. Reason (R): In a right triangle, ta

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Other Competitive Exams

NDA

NDA

MATHS

Courses

Class Room Courses
Online Live Courses
Online Recorded Courses

ONLINE COURSES

More

Solution

Q.
Assertion (A): If the ratio of the height of a pole and its shadow is $\sqrt{3} : 1$ , then the Sun’s altitude is $30 °$ .

Reason (R): In a right triangle, $t a n θ = \frac{p}{b}$ , where p stands for perpendicular (opposite side to angle θ) and b for base (adjacent side).

1 Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

2 Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A)

3 Assertion (A) is true but reason (R) is false.

4 Assertion (A) is false but reason (R) is true.

Ans.
(4)

Let AB be the pole and BC be its shadow on the ground.

Here,

$A B : B C = \sqrt{3} : 1 and let ∠ A C B = θ . I n ∆ A B C, w e h a v e : t a n θ = \frac{A B}{B C} = \frac{\sqrt{3}}{1} = \sqrt{3} \Rightarrow t a n θ = t a n 60 ° \Rightarrow θ = 60 ° \Rightarrow {S u n ’ s a l t i t u d e i s 60 \circ .$

Hence, Assertion (A) is false.

Also, the fact given under Reason (R) is the definition of tangent. So, Reason (R) is true.

Want Us to Email you About Special Offers & Updates?