Question

a ladder 6 m long leans against a building the ladder from angle of 60 degree with the ground at what height of the building does the ladder reach also find the horizontal distance from the foot of the ladder of the base of the building​

Answer 1

Answer:

The shorter sides a and b are such that their squares are equal to the square of the longest side c, which is 6 meters long

a^2+b^2=36

The ratio of a to b is 1 to 2, for all 30 60 90 triangles

so we further know a=2b

We can thus substitute

(2b)^2+b^2=36

That’s 4b^2+b^2=36

5b^2=36

b^2=36/5

The negative solution isn’t important here.

That’s about 2.68 meters out from the wall

The height is twice that, about 5.37 meters up the wall

Checking our work.

2.68^2+5.37^2=36.0193

The square root of 36 is 6. The extra tiny bit is due to our rounding to two digits.

Seems reasonably legit.