Advertisements
Advertisements
Question
What is the distance between the points (5 sin 60°, 0) and (0, 5 sin 30°)?
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
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
Let ABCD be a square of side 2a. Find the coordinates of the vertices of this square when The centre of the square is at the origin and coordinate axes are parallel to the sides AB and AD respectively.
Find the third vertex of a triangle, if two of its vertices are at (−3, 1) and (0, −2) and the centroid is at the origin.
Three consecutive vertices of a parallelogram are (-2,-1), (1, 0) and (4, 3). Find the fourth vertex.
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.
Show that the points A(3,0), B(4,5), C(-1,4) and D(-2,-1) are the vertices of a rhombus. Find its area.
Find the area of a quadrilateral ABCD whose vertices area A(3, -1), B(9, -5) C(14, 0) and D(9, 19).
Find the area of quadrilateral PQRS whose vertices are P(-5, -3), Q(-4,-6),R(2, -3) and S(1,2).
If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
The co-ordinates of point A and B are 4 and -8 respectively. Find d(A, B).
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
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 three points (x1, y1) (x2, y2), (x3, y3) lie on the same line, prove that \[\frac{y_2 - y_3}{x_2 x_3} + \frac{y_3 - y_1}{x_3 x_1} + \frac{y_1 - y_2}{x_1 x_2} = 0\]
What is the area of the triangle formed by the points O (0, 0), A (6, 0) and B (0, 4)?
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
If the points (k, 2k), (3k, 3k) and (3, 1) are collinear, then k
If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =
Point P(– 4, 2) lies on the line segment joining the points A(– 4, 6) and B(– 4, – 6).
