The bottom of a ladder is on horizontal ground.

Question

The top of a ladder is leaning against a vertical wall.

Diagram: right angle triangle labelled height is h metres, bottom of triangle is labelled d metres and in between the labelled h and d metres there is a 90 degrees angle. There is an angle to the left of that also next to d which is labelled x.

Carrying on question:

The bottom of the ladder is d metres from the wall. The top of the ladder is h metres above the ground. The angle between the ladder and the ground is x degrees.

Some safety instructions say it is safe to climd the ladder when:
h=4d

a) Work out the value of x when h=4d.

My working out:
1)c^2=a^2+b^2
2)hypotenuse is c so it equals the h metres squared multiplied by the d metres quared.

I have no clue after that please help.

Part b of this question:

Some different safety instructions say the angle between the ladder and the ground should be 75 degrees. the ladder is moved so that x=75 degrees

How does this affect the height, h metres, of the top of the ladder above the ground?

My answer:

The angle is higher so the height is higher.

I am not really sure about part a and part b please help

Answer 1

tan(x) = h/d = 4d/d = 4
x = arctan(4) = 76°

for part b, h decreases, because x decreases.

Answer 2

dont know mate