Advertisements
Advertisements
प्रश्न
The distance between the points (a cos 25°, 0) and (0, a cos 65°) is
पर्याय
a
2a
3a
None of these
Advertisements
उत्तर
We have to find the distance between A(a cos 25°, 0) and B (0 , a cos 65° ) .
In general, the distance between A(x1 , y1 ) and B( x2 ,y2 ) is given by,
`AB = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`
So,
\[AB = \sqrt{\left( 0 - a\cos25° \right)^2 + \left( a\cos65° - 0 \right)^2}\]
\[ = \sqrt{\left( a\cos25° \right)^2 + \left( a\cos65° \right)^2}\]
But according to the trigonometric identity,
`sin^2 theta + cos^2 theta = 1`
Therefore,
AB = a
APPEARS IN
संबंधित प्रश्न
How will you describe the position of a table lamp on your study table to another person?
Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.
Find the coordinates of the circumcentre of the triangle whose vertices are (3, 0), (-1, -6) and (4, -1). Also, find its circumradius.
Find the coordinates of the point which divides the line segment joining (−1,3) and (4, −7) internally in the ratio 3 : 4
Find the ratio in which the point (2, y) divides the line segment joining the points A (-2,2) and B (3, 7). Also, find the value of y.
The line segment joining the points P(3, 3) and Q(6, -6) is trisected at the points A and B such that Ais nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.
If the poin A(0,2) is equidistant form the points B (3, p) and C (p ,5) find the value of p. Also, find the length of AB.
If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
The perpendicular distance of the point P (4, 3) from x-axis is
ABCD is a parallelogram with vertices \[A ( x_1 , y_1 ), B \left( x_2 , y_2 \right), C ( x_3 , y_3 )\] . Find the coordinates of the fourth vertex D in terms of \[x_1 , x_2 , x_3 , y_1 , y_2 \text{ and } y_3\]
In \[∆\] ABC , the coordinates of vertex A are (0, - 1) and D (1,0) and E(0,10) respectively the mid-points of the sides AB and AC . If F is the mid-points of the side BC , find the area of \[∆\] DEF.
If A (1, 2) B (4, 3) and C (6, 6) are the three vertices of a parallelogram ABCD, find the coordinates of fourth vertex D.
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
If the centroid of the triangle formed by (7, x) (y, −6) and (9, 10) is at (6, 3), then (x, y) =
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
If P(2, 4), Q(0, 3), R(3, 6) and S(5, y) are the vertices of a parallelogram PQRS, then the value of y is
Students of a school are standing in rows and columns in their playground for a drill practice. A, B, C and D are the positions of four students as shown in figure. Is it possible to place Jaspal in the drill in such a way that he is equidistant from each of the four students A, B, C and D? If so, what should be his position?
The point at which the two coordinate axes meet is called the ______.
The distance of the point (3, 5) from x-axis (in units) is ______.
