Bissoy.com
Doctors Medicines MCQs Q&A

One side of a triangle and a rectangle is the same. The third vertex of the triangle lies on the midpoint of the rectangle side opposite the common side. The rectangle sides are in the ratio 2 : 3 and the common side is the longer side of the rectangle.  What is the sin value of the angle between the common side and the equal side of the triangle?

One side of a triangle and a rectangle is the same. The third vertex of the triangle lies on the midpoint of the rectangle side opposite the common side. The rectangle sides are in the ratio 2 : 3 and the common side is the longer side of the rectangle.  What is the sin value of the angle between the common side and the equal side of the triangle? Correct Answer 4/5

Calculation:

Let 2a and 3a are sides of the rectangle, the triangle and rectangle will be as shown in the figure,

[ alt="F1 ravisharma Nishad 21.04.21 D5" src="//storage.googleapis.com/tb-img/production/21/04/F1_ravisharma_Nishad_21.04.21_D5.png" style="width: 141px; height: 133px;">

The three angles are ∠ AEC, ∠ EAC and ∠ ECA.

∠ EAC = ∠ECA  (∵  Δ AEC is an isosceles triangle with AE = EC)

Sin (∠ EAC) = 2a/EA

EA2 = (2a)2 + (1.5a)2 = 6.25a2

⇒ EA = 2.5a

∴ Sin (∠ EAC) = 2a/2.5a = 4/5

Related Questions

Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?
The value of the expression:sin21° + sin211° + sin221° + sin231° + sin241° + sin245° + sin249° + sin259° + sin269° + sin279° + sin289° is?
A square ABCD, L is the midpoint of side AB, M is the midpoint of side BC, N is the midpoint of side CD and O is the midpoint of side AD, then find the ratio of area of shaded region PQRS to the area of square ABCD.
A person wants to visit some places. He starts from a vertex and then wants to visit every vertex till it finishes from one vertex, backtracks and then explore other vertex from same vertex. What algorithm he should use?
What will be the ratio between the area of a triangle and area of a rectangle with having one of the sides of rectangle as base of the triangle and a vertex of the triangle on the opposite side of the rectangle?
Let G be a directed graph whose vertex set is the set of numbers from 1 to 100. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. The minimum number of edges in a path in G from vertex 1 to vertex 100 is 
Let G be a directed graph whose vertex set is the set of numbers from 1 to 50. There is an edge from a vertex i to a vertex j if and only if either j = i + 1 or j = 3i. Calculate the minimum number of edges in a path in G from vertex 1 to vertex 50.
From a rectangular sheet of paper of length 24 cm and breadth 18 cm, a triangle is cut in such a way that one of the lengthier sides becomes the base of the triangle and the vertex of the triangle lies 3 cm below the opposite lengthier side of the rectangle, then what is the area of the triangle?
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
Two right angled triangles are congruent if :
I. The hypotenuse of one triangle is equal to the hypotenuse of the other.
II. A side for one triangle is equal to the corresponding side of the other.
III. Sides of the triangles are equal.
IV. An angle of the triangle are equal.
Of these statements, the correct ones are combination of: