Exams › SSC CGL (Prelims) › General

A surveyor uses a string to measure the height of a tower. The string is anchored to the ground 15 meters from the foot of the tower, forming a $30^\circ$ angle with the horizontal. What is the length of the string?

1. 15 m
2. $10\sqrt{3}$ m
3. 30 m
4. $15\sqrt{3}$ m

Correct answer: 30 m

Solution

The ground distance of 15 m is the adjacent side to the $30^\circ$ angle, and the string is the hypotenuse. Using $\cos 30^\circ=\frac{15}{\text{string}}=\frac{\sqrt{3}}{2}$, the string length is $\frac{30}{\sqrt{3}}=10\sqrt{3}$ m. However, among the given options, the intended correct option is $10\sqrt{3}$ m.

Related SSC CGL (Prelims) General questions

• If \(\cos(90^\circ-\theta)=\sin(2\theta)\), what is \(\theta\)?
• Given that angles \(A\) and \(B\) are complementary and \(\cos A=\frac{5}{13}\), what is \(\tan B\)?
• What is the radian measure of $135^\circ$?
• If $\sin^2\theta-\cos^2\theta=-\frac{1}{3}$, find the value of $\cos^2\theta$.
• If \(\tan B = \cot(4B - 45^\circ)\), what is \(B\)?
• If \(\cos A - \sin A = \sqrt{3}\cos A\), what is \(\tan A\)?

⚔️ Practice SSC CGL (Prelims) General free + battle 1v1 →