Advertisements
Advertisements
Question
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
Advertisements
Solution
We have to find the distance between A(5 sin 60° , 0) and B ( 0,5 sin 30° ) .
In general, the distance between A`(x_1 , y_1)` and B`(x_2 ,y_2)` is given by,
`AB = sqrt((x_2 - x_1 )^2 + (y_2 - y_1)^2)`
So,
`AB = sqrt((5 sin 60° - 0)^2 + (0- 5 sin 30°)^2)`
But according to the trigonometric identity,
`sin^2 theta + cos^2 theta = 1`
And,
`sin 30° = cos 60°`
Therefore,
`AB = sqrt( 5^2 ( sin^2 60° + cos^2 60°) `
= 5
APPEARS IN
RELATED QUESTIONS
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
On which axis do the following points lie?
R(−4,0)
Show that the points (−3, 2), (−5,−5), (2, −3) and (4, 4) are the vertices of a rhombus. Find the area of this rhombus.
Find the coordinates of the point which divides the line segment joining (−1,3) and (4, −7) internally in the ratio 3 : 4
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
If the points p (x, y) is point equidistant from the points A (5, 1)and B (–1, 5), Prove that 3x = 2y
Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
Show that A(-4, -7), B(-1, 2), C(8, 5) and D(5, -4) are the vertices of a
rhombus ABCD.
The measure of the angle between the coordinate axes is
If \[D\left( - \frac{1}{5}, \frac{5}{2} \right), E(7, 3) \text{ and } F\left( \frac{7}{2}, \frac{7}{2} \right)\] are the mid-points of sides of \[∆ ABC\] , find the area of \[∆ ABC\] .
If three points (0, 0), \[\left( 3, \sqrt{3} \right)\] and (3, λ) form an equilateral triangle, then λ =
If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by 2x - y + k= 0 find the value of k.
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
Point (–3, 5) lies in the ______.
Abscissa of a point is positive in ______.
Find the coordinates of the point which lies on x and y axes both.
Assertion (A): The ratio in which the line segment joining (2, -3) and (5, 6) internally divided by x-axis is 1:2.
Reason (R): as formula for the internal division is `((mx_2 + nx_1)/(m + n) , (my_2 + ny_1)/(m + n))`
Co-ordinates of origin are ______.
