Review question

# Given a picture hanging from a wall, can we find these angles? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5533

## Question

A rectangular picture of width $\quantity{32}{cm}$ and height $\quantity{20}{cm}$ has its lower edge $AB$ horizontal against a vertical wall. It hangs at an angle of $15^\circ$ to the wall and may be taken to be of negligible thickness. It is supported by two equal strings $FD$, $FC$ of length $\quantity{20}{cm}$ attached to the upper corners $C$, $D$ of the picture and to a point $F$ on the wall vertically above the centre of $AB$.

Copy the given sketch, including the projections of $C$, $D$ and $E$, the mid-point of $CD$, onto the wall at $X$, $Y$ and $Z$ respectively.

Identify in terms of the letters the following angles and calculate them:

1. the angle between the two strings,
2. the angle between the string $DF$ and the wall,
3. the angle between the wall and the plane containing both strings.