Trigonometric Ratios

Q. A man standing on a level plane observes the elevation of the top of a pole to be $\theta$. If he walks a distance equal to double the height of the pole towards the pole, the angle of elevation becomes $2\theta .$ Then the value of $\theta$ (in degrees) is

Q. An altitude $BD$ and angular bisector $BE$ are drawn in $△ABC$ from the vertex $B.$ It is known that the length of side $AC=1$ and the magnitude of angle $BEC,ABD,$ $ABE,BAC$ form an arithmetic progression. Let $B^{\prime }$ be the image of point $B$ with respect to side $AC$ of $△ABC$. If the length $B{B}^{\prime }$ is equal to $\sqrt{\frac{a}{b}};$ where $a,b\in N,$ then the least possible value of $a+b$ is

Q. If $cosA=\frac{4}{5}$, then the value of tan A is:

[1 Mark]
[Trigonometric Ratios]
[NCERT Exemplar]

$\frac{3}{5}$

1. $\frac{4}{3}$
2. $\frac{3}{5}$
3. $\frac{5}{3}$
4. $\frac{3}{4}$

Q.
In the figure given above, what is the value of $tan\theta$ in terms of a, b and c?

1. $\frac{b}{a}$
2. $\frac{a}{b}$
3. $\frac{b}{c}$
4. $\frac{c}{a}$

Q. Find the values of $cot\theta andcosec\theta$ in the figure given above.

1. $2,\frac{5}{2}$
2. $\frac{4}{3},\frac{5}{3}$
3. $\frac{5}{2},2$
4. $2,\frac{5}{4}$

Q.
Find the length of side AC.

1. $sin\theta$
2. $\sqrt{3}sin\theta$
3. $\frac{sin\theta }{\sqrt{3}}$
4. $\sqrt{3}{sin}^2\theta$

Q. A right angled triangle $\Delta ABC$ is right angled at C with sides AB = 10 cm and AC = 6 cm. Find cosine of $\angle$B.

1. $\frac{7}{10}$
2. $\frac{6}{10}$
3. $\frac{4}{5}$
4. $\frac{3}{5}$

Q. $\Delta ABC$ is right angled at C. Find cos B.

1. $\frac{AC}{AB}$
2. $\frac{AC}{BC}$
3. $\frac{AB}{BC}$
4. $\frac{BC}{AB}$

Q. If triangle ABC is right angled at B and
$sinA=\frac{3}{5}$, then find the value of cos A.

1. $\frac{3}{5}$
2. $\frac{5}{4}$
3. $\frac{4}{5}$
4. $\frac{5}{3}$

Q. In a triangle ABC right angled at B,
$\angle ACB=\theta .$

$\text{If}tan\theta =\frac{5}{12}$,
$\text{then find the value of}\frac{(1+cos\theta )\times (1-sin\theta )}{(1+sin\theta )\times (1-cos\theta )}.$

1. $\frac{91}{18}$
2. $\frac{100}{9}$
3. $\frac{12}{5}$
4. $\frac{84}{27}$