Find the volume of a trough 5 meters long whose ends are equilateral triangles, each of whose
sides has a length of 2 meters.

Step-by-step explanation:

we know that

The volume of a trough is equal to

where

B is the area of equilateral triangle

L is the length of a trough

step 1

Find the area of  equilateral triangle B

The area of a equilateral triangle applying the law of sines is equal to

where

substitute

step 2

Find the volume of a trough

we have

substitute

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

6: 07 is your answer

step-by-step explanation: