Slope of Line Using Trigonometry

Q. Slope of a line which makes an angle ${60}^{\circ }$ with the positive direction of the X-axis is _____.

1. 1
2. 0
3. $\sqrt{3}$
4. $\sqrt{2}$

Q. Slope of a line which makes an angle ${30}^{\circ }$ with the positive direction of the X-axis is _____.

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

Q. If a line makes an angle of 60° with the positive direction of x-axis in the anticlockwise direction, the slope of the line is

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

Q. A line makes an angle of ${60}^{\circ }$ with the positive direction of the x-axis. The slope of the line is _____.

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

Q. A line makes an angle of ${60}^{\circ }$ with the positive direction of the x-axis. The slope of the line is

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

Q. A line makes an angle of ${30}^o$ with the positive direction of $X$ axis. What is the slope of line.

1. $\frac{1}{2}$
2. $\sqrt{3/2}$
3. $\sqrt{3}$
4. $1\sqrt{3}$

Q.
If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then $\angle$TOP is ____.

1. ${30}^0$
2. ${60}^0$
3. ${120}^0$
4. ${90}^0$

Q. A line makes an angle of ${30}^{\circ }$ with the positive direction of the x-axis. The slope of the line is _____.

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

Q. If A(7, 5) , B(4, 3) and C(-2, -3) are the vertices of a triangle, then find the slope angle, $\theta$ of side BC.

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. $0^{\circ }$

Q.

Refer to the following figure:

Which line segment depicts the “height” of point A from the base BE?

Given that ∠ADE = ${90}^{\circ }$ and ∠ABC = ∠AEB

__

Q. Match the given angles with the corresponding slopes.(Angles are with respect to positive direction of x-axis)

1. \N
2. $\sqrt{3}$
3. $\frac{1}{\sqrt{3}}$
4. Not defined

Q. $T:R^2\to R^2$ first rotates points through $-\frac{3\pi }{4}$ radian (clockwise) and then reflects points through horizontal x-axis.

Q. The angle made by the line $\sqrt{3}x-y+3=0$ with the positive direction of X-axis is

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q. A line makes an angle of ${90}^{\circ }$ with the positive direction of the x-axis. The slope of the line is _____.

1. $\frac{1}{\sqrt{2}}$
2. $\frac{1}{\sqrt{3}}$
3. 1
4. Cannot be determined

Q. The cosine ratio of an angle made by the line with the positive direction of X-axis is called the slope of that line

1. True
2. False

Q. Slope of a line which makes an angle ${45}^{\circ }$ with the positive direction of the X-axis is _____.

1. 1
2. 0
3. $\sqrt{3}$
4. $\sqrt{2}$