There is a 2.8 m long staircase against the wall at an angle of 60 degrees

| March 10, 2021 | education

There is a 2.8 m long staircase against the wall at an angle of 60 degrees to the horizon. How many meters is the lower end of the staircase from the wall?

The staircase standing against the wall, together with the wall, forms a right-angled triangle ABC, in which side AB is a staircase, its length is 2.8 m, side BC is a wall, side AC is the distance of the lower end of the stairs from the wall, angle to the horizon – this is ∠BAC (∠BAC = 60 °).

Let’s find the size of the angle ABC, taking into account that the sum of all the angles of any triangle is 180 °:

180 – 90 – 60 = 90 – 60 = 30 °.

Let us find the length of the AC side, taking into account that in a right-angled triangle the leg, which lies opposite the angle of 30 °, is equal to half of the hypotenuse:

2.8: 2 = 1.4 m.

Answer: The bottom end of the ladder is 1.4 m from the wall.



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