# Thread: Trigonometry Problem: Possibly Using the Ratios

1. ## Trigonometry Problem: Possibly Using the Ratios

Hello. I am back with another trigonometry question. Any help with the following problem would be greatly appreciated.

A stepladder stands on a floor, with its feet 1.5 metres apart. If the angle formed by the legs is 55 degrees, how high above the floor is the top of the ladder?

I have tried dropping a perpendicular line from the top of the stepladder to the floor, and then applying various trigonometric ratios; this did not work. I have also tried putting the angle in different places. The best answer I could obtain was 1.46 metres; the real answer is 1.44 metres.

Thank you!

Hello. I am back with another trigonometry question. Any help with the following problem would be greatly appreciated.

A stepladder stands on a floor, with its feet 1.5 metres apart. If the angle formed by the legs is 55 degrees, how high above the floor is the top of the ladder?

I have tried dropping a perpendicular line from the top of the stepladder to the floor, and then applying various trigonometric ratios; this did not work. I have also tried putting the angle in different places. The best answer I could obtain was 1.46 metres; the real answer is 1.44 metres.

Thank you!

The ladder forms an isosceles triangle (if both sides are the exact same length, which they normally are).

Hence the angle the ladder makes with the floor is the same at both legs.
This angle is

$\displaystyle \frac{180^o-55^o}{2}=\frac{125^o}{2}=62.5^o$

Hence

$\displaystyle tan(62.5^o)=\frac{h}{(0.5)1.5}\ \Rightarrow\ h=0.75tan(62.5^o)m=1.44m$

Alternatively, draw the perpendicular height and halve the angle at the top...

$\displaystyle tan(27.5^o)=\frac{0.75}{h}\ \Rightarrow\ h=\frac{0.75}{tan(27.5^o)}=1.44m$