Question

The distance between two buildings is $24\text{m}$. The heights of the buildings are $12\text{m}$ and $22\text{m}$. Find the distance between the tops (in $\text{m}$).

• A. $20$
• B. $26$
• C. $30$
• D. $32$

Answer 1

The correct option is B $26$

From the diagram, $PB=CD=12\text{m}$
$AP=AB-PB=(22-12)\text{m}=10\text{m}$
Also $CP=BD=24\text{m}$
Since $△APC$ is a right angled triangle,
${AC}^2={AP}^2+{PC}^2$
${AC}^2={10}^2+{24}^2$
${AC}^2=676$
$\therefore AC=26\text{m}$
Hence, distance between their tops is $26\text{m}$.