Question : The ratio of the length of a rod and its shadow is $1: \sqrt{3}$. The angle of elevation of the sun is:
Option 1: $90^{\circ}$
Option 2: $30^{\circ}$
Option 3: $45^{\circ}$
Option 4: $60^{\circ}$
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Correct Answer: $30^{\circ}$
Solution : The ratio of the length of a rod and its shadow, $\frac{AB}{BC} = \frac{1}{\sqrt{3}}$ ⇒ $\tan \theta = \frac{AB}{BC}$ ⇒ $\tan \theta = \frac{1}{\sqrt{3}}$ ⇒ $\tan\theta = \tan 30^{\circ}$ ⇒ $\theta =30^{\circ}$ Hence, the correct answer is $30^{\circ}$.
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Question : In a $\triangle ABC$, if $2\angle A=3\angle B=6\angle C$, then the value of $\angle B$ is:
Option 1: $60^{\circ}$
Option 4: $90^{\circ}$
Question : If a pole of 12 m height casts a shadow of $4\sqrt{3}$ m long on the ground, then the sun's angle of elevation at that instant is:
Option 1: 30°
Option 2: 60°
Option 3: 45°
Option 4: 90°
Question : Find the value of $\cos 0^{\circ}+\cos 30^{\circ}-\tan 45^{\circ}+\operatorname{cosec} 60^{\circ}+\cot 90^{\circ}$.
Option 1: $\frac{7}{6 \sqrt{3}}$
Option 2: $\frac{\sqrt{3}}{6}$
Option 3: $\frac{7}{6}$
Option 4: $\frac{7}{2 \sqrt{3}}$
Question : If the angle of elevation of the sun changes from 45° and 65°, then the length of the shadow of a pillar decreases by 10 m. The height of the pillar is:
Option 1: $5\left (3-\sqrt{3} \right)$ m
Option 2: $5\left (\sqrt{3}+1 \right)$ m
Option 3: $15\left (\sqrt{3}+1 \right)$ m
Option 4: $5\left (3+\sqrt{3} \right)$ m
Question : If $\cos(A+B)=0$ and $\sin(A-B)=0$, then what is the value of $\angle A$ and $\angle B$ ? ( $0^\circ < A, B \leq 90 ^\circ$)
Option 1: $20^\circ, 70^\circ$
Option 2: $45^\circ, 45^\circ$
Option 3: $60^\circ, 30^\circ$
Option 4: $15^\circ, 75^\circ$
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