Quantitative Aptitude

Trigonometry

435 Questions
All Height and Distance 268 Triangle Properties and Rules 50 Standard Angle Evaluation 33 Complementary and Odd-Even Angles 30 Value of one ratio from another 26 Trigonometric Identities 14 Maxima and Minima 6 General and Principal Solutions 5 Quadratic Substitution 3

Trigonometry Questions

Multiple choice

Let $10$ vertical poles standing at equal distances on a straight line, subtend the same angle of elevation $\alpha$ at a point $O$ on this line and all the poles are on the same side of $O$. If the height of the longest pole is $h$ and the distance of the foot of the smallest pole from $O$ is $a$; then the distance between two consecutive poles, is
  1. $\displaystyle \frac{h \sin \alpha + a \cos \alpha}{9 \cos \alpha}$
  2. $\displaystyle \frac{h \cos \alpha - a \sin \alpha}{9 \sin \alpha}$
  3. $\displaystyle \frac{h \sin \alpha + a \cos \alpha}{9 \sin \alpha}$
  4. $\displaystyle \frac{h \cos \alpha - a \sin \alpha}{9 \cos \alpha}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the poles be at distances x1, x2, ..., x10 from O. tan(alpha) = h_i / x_i. x_i = h_i / tan(alpha). The distance between consecutive poles is (h_{i+1} - h_i) / tan(alpha). Using the geometry of the setup, the formula simplifies to the given expression.

Multiple choice

In the given triangle $AB=3cm$ and $AC=5cm$. Find all trignometric ratios.
  1. $\sin {\theta}=\cfrac{P}{H}=\cfrac{4}{5}$

    $\cos {\theta}=\cfrac{B}{H}=\cfrac{4}{5}$

    $\tan {\theta}=\cfrac{P}{B}=\cfrac{4}{3}$

    $\cot{\theta}=\cfrac{B}{P}=\cfrac{3}{4}$

    $\sec {\theta}=\cfrac{H}{B}=\cfrac{5}{3}$

    $co\sec {\theta}=\cfrac{H}{P}=\cfrac{5}{4}$
  2. $\sin {\theta}=\cfrac{P}{H}=\cfrac{4}{5}$

    $\cos {\theta}=\cfrac{B}{H}=\cfrac{2}{5}$

    $\tan {\theta}=\cfrac{P}{B}=\cfrac{4}{3}$

    $\cot{\theta}=\cfrac{B}{P}=\cfrac{3}{4}$

    $\sec {\theta}=\cfrac{H}{B}=\cfrac{5}{3}$

    $co\sec {\theta}=\cfrac{H}{P}=\cfrac{5}{4}$
  3. $\sin {\theta}=\cfrac{P}{H}=\cfrac{4}{5}$

    $\cos {\theta}=\cfrac{B}{H}=\cfrac{1}{5}$

    $\tan {\theta}=\cfrac{P}{B}=\cfrac{4}{3}$

    $\cot{\theta}=\cfrac{B}{P}=\cfrac{3}{4}$

    $\sec {\theta}=\cfrac{H}{B}=\cfrac{5}{3}$

    $co\sec {\theta}=\cfrac{H}{P}=\cfrac{5}{4}$
  4. $\sin {\theta}=\cfrac{P}{H}=\cfrac{4}{5}$

    $\cos {\theta}=\cfrac{B}{H}=\cfrac{3}{5}$

    $\tan {\theta}=\cfrac{P}{B}=\cfrac{4}{3}$

    $\cot{\theta}=\cfrac{B}{P}=\cfrac{3}{4}$

    $\sec {\theta}=\cfrac{H}{B}=\cfrac{5}{3}$

    $co\sec {\theta}=\cfrac{H}{P}=\cfrac{5}{4}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

An electrician has to repair an electric fault on a pole of height $5$m. She needs to reach a point $1.3$m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of $60^0$ to the horizontal, would enable her to reach the required position? Also, how far the foot of the pole should she place the foot of the ladder? ( You may take $\sqrt3=1.73$).
  1. $\text{length of ladder}=7.4m$ , $\text{distance}=2.14m$
  2. $\text{length of ladder}=4.27m$ , $\text{distance}=3.7m$
  3. $\text{length of ladder}=4.27m$ , $\text{distance}=2.14m$
  4. $\text{length of ladder}=4.7m$ , $\text{distance}=2.14m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Height to reach = 5 - 1.3 = 3.7m. Ladder length L = 3.7 / sin(60) = 3.7 / (sqrt(3)/2) = 7.4 / 1.73 = 4.277m. Distance from pole = 3.7 / tan(60) = 3.7 / 1.73 = 2.138m.

Multiple choice

Assertion ($A$): The angles of elevation of a tower from two points which are at distances $12$ m and $64$ m from the foot of the tower on the opposite sides are complementary. The height of the tower is $24$ m. Reason ($R$): The angles of elevation of a tower from two points which are at distances $a$' and $b$' from the foot of the tower are complementary, then the height of the tower is $\sqrt{ab}$.
  1. $A$ and $R$ both are true,$R$ is correct explanation for $A$
  2. Both $A$ and $R$ are true and $R$ is not correct explanation of $A$
  3. $A$ is true but $R$ is false
  4. $A$ is false but $R$ is true.
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Assertion (A): The shadow of a tower on a level plane is found to be 60 meters longer when sun's altitude is $30^{0}$ than that when it is $45^{0}$ Then the height of the tower is $30$ $(\sqrt{3}+1)$ {meters} Reason (R): The angle of elevation of a top of a tower standing an horizontal plane from a Point $A$ is $\alpha$. After wlaking a distance $d$ meters towards the foot of the tower, the angle elveation is found to be $\beta$ then the height of the tower is $h=\displaystyle \frac{d}{\cot\alpha-\cot\beta}$
  1. Both $A$ and $R$ are ture and $R$ is the correct explanation of $A$
  2. Both $A$ and $R$ are true and  $R$ is not correct explanation of $A$
  3. $A$ is true but $R$ is false
  4. $A$ is false but $R$ is true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The height h = d / (cot(30) - cot(45)) = 60 / (sqrt(3) - 1) = 60(sqrt(3)+1) / 2 = 30(sqrt(3)+1). Both the assertion and the reason are correct, and the reason provides the formula used in the assertion.

Multiple choice

Manan observes that the angle of elevation of the top $P$ of the tower $OP$ at a point $A$ on the ground is $\alpha$, he then walks a distance $AB$ towards the foot $O$ of the tower and finds the angle of elevation as $\beta$, he again walks a distance $BC$ in the same direction and observes the angle of elevation now is $\gamma$. He notices that $a + \beta + \gamma = 180^o; \alpha, \beta, \gamma$ are in A.P. and the distance of $C$ from the foot of the tower is half the distance of $B$ from the foot $O$ of the tower. If the height of tower is $h$, the distance of $A$ from the foot $O$ is $\dfrac{5h}{3\sqrt{3}}$.

  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

  2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

  3. Assertion is correct but Reason is incorrect

  4. Assertion is incorrect but Reason is correct
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

ABC is a vertical tower of height H. The angle of elevation of B from a point P, which is at a distance of 2a from the foot of the tower A, is 30° and the angle of elevation of C from a point Q, which is at a distance of 'a' from A, is 60°. What is the ratio of AB to BC?

  1. 1 : 1

  2. 3 : 1

  3. 1 : 2

  4. 2 : 1

  5. 1 : 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In triangle PAB, tan(30) = H / 2a, so H = 2a * tan(30) = 2a / sqrt(3). In triangle QAC, tan(60) = (H+BC) / a, so H+BC = a * tan(60) = a * sqrt(3). Thus, BC = a * sqrt(3) - 2a / sqrt(3) = (3a - 2a) / sqrt(3) = a / sqrt(3). The ratio AB/BC = H/BC = (2a/sqrt(3)) / (a/sqrt(3)) = 2/1.