Introduction to Trigonometry

Q.

In the right triangle ABC, which of the following side is termed as "adjacent side" with respect to the angle $\theta$?

1. BC

2. AC

3. Any side

4. AB

Q.

In a right angled triangle ABC (right angled at B), find the value of tan A × tan C.
[2 Marks]

Q. The value of
$tan{48}^{\circ }.tan{23}^{\circ }.tan{42}^{\circ }.tan{67}^{\circ }$ is equal to

1. 0
2. 1
3. 2
4. 4

Q.

In triangle ABC, right angled at B, if $\angle$A is made larger and larger till it becomes ${90}^{\circ }$, what can you say about AC and AB if BC = 1 unit?

1. 0, 1

2. 1, 1

3. 1 , 0

4. 0, 0

Q.
ABCD is a rectangle such that $\angle CAB={60}^{\circ }$ and $AC=aunits$.
Find the area of rectangle ABCD.

1. $\frac{\sqrt{3}}{2}{a}^2$

2. $\frac{\sqrt{2}}{3}{a}^2$

3. $\frac{\sqrt{3}}{4}{a}^2$
4. $\frac{\sqrt{3}}{8}{a}^2$

Q.

In $\Delta$ABC, right angled at B, if $\angle A$ is made smaller and smaller till it becomes zero, find the value of sin A and cos A.

1. 0, $\sqrt{3}$

2. 0, 1

3. 0, Not defined

4. Not defined, 0

Q. Angle of elevation of the top of a tower is 45 degree. Find its height if it is 20 m away.

1. 50 m
2. 40 m
3. 20 m
4. 30 m

Q. A 15 m high building casts a shadow 15 m long. Find the angle of elevation of the Sun.

1. 30 degree
2. 45 degree
3. 15 degree
4. 60 degree

Q. In a right angled triangle ABC right angled at B,
$5\times sinA=3$.
Find the value of cosC + tanA + cosecC.

1. $\frac{12}{15}$
2. $\frac{13}{12}$
3. $\frac{13}{5}$
4. $\frac{12}{5}$

Q. Find the angle of depression in the given figure.

1. 60 degree
2. 90 degree
3. 45 degree
4. 30 degree