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Worksheet: Angle between Two Straight Lines in Two Dimensions
Q2:
Determine the measure of the positive angle that the straight line makes with the positive direction of the -axis approximated to the nearest second, given that passes through points and .
- A
- B
- C
- D
- E
Q3:
If the acute angle between the straight lines whose equations are and is , find all the possible values of .
- A , 7
- B ,
- C , 1
- D , 16
Q4:
Given that is a right triangle at , the equation of is , and the equation of is , find approximated to the nearest minute.
- A
- B
- C
- D
Q5:
Determine, to the nearest second, the measure of the positive angle that the straight line makes with the positive -axis.
- A
- B
- C
- D
Q6:
A line passing through makes an angle with the line , and . What is the equation of this line?
- A ,
- B ,
- C ,
- D ,
Q7:
Determine, to the nearest second, the measure of the acute angle between two straight lines having gradients of 5 and .
- A
- B
- C
- D
Q8:
Determine, to the nearest second, the measure of the acute angle between two straight lines having gradients of 7 and .
- A
- B
- C
- D
Q9:
Determine, to the nearest second, the measure of the acute angle between two straight lines having gradients of and .
- A
- B
- C
- D
Q10:
Find the size of the acute angle between the two straight lines whose equations are and to the nearest second.
- A
- B
- C
- D
Q11:
Find the size of the acute angle between the two straight lines whose equations are and to the nearest second.
- A
- B
- C
- D
Q12:
Determine the size of the acute angle between the two straight lines and to the nearest second.
- A
- B
- C
- D
Q13:
Determine the size of the acute angle between the two straight lines and to the nearest second.
- A
- B
- C
- D
Q14:
Let be the angle between two lines that pass through . If and the gradients of the lines are and , with , find the equations of these lines.
- A
- B
- C
Q15:
Find, to the nearest second, the measure of the acute angle included between the straight line and the straight line whose gradient is .
- A
- B
- C
- D
Q16:
Let be the line on points and , and the perpendicular to that passes through the origin . What is the size of the positive angle that makes with the positive -axis? Give your answer to the nearest second.
- A
- B
- C
- D
Q17:
Determine, to the nearest second, the size of the positive angle that the straight line , makes with the positive -axis.
- A
- B
- C
- D
Q18:
Determine, to the nearest second, the size of the positive angle made with the positive -axis by the perpendicular straight line to the straight line .
- A
- B
- C
- D
Q19:
Find the size of the acute angle between and approximated to the nearest second.
- A
- B
- C
- D
Q20:
Find, to the nearest second, the size of the angle between the line and the positive -axis.
- A
- B
- C
- D
Q21:
Find the size of the acute angle that lies between the straight line whose direction vector is , and the straight line whose equation is in degrees, minutes, and the nearest second.
- A
- B
- C
- D
Q22:
Find the size of the acute angle between and the -axis approximated to the nearest second.
- A
- B
- C
- D
Q23:
If is the measure of the acute angle between the two straight lines whose equations are and and , find all the possible values of .
- A
- B
- C
- D
Q24:
If points , , and form a right triangle at , find the value of , and then determine the measures of the other two angles to the nearest second.
- A , ,
- B , ,
- C , ,
- D , ,
Q25:
Find the size of the acute angle between the following pair of straight lines: and .
- A
- B
- C
- D