Final 2 - Height of the Church

Given:

• $\mbox{Observer #1 is at ground level}$
• $\mbox{Sees the top of  head of Observer #2 and top of church in line.}$
• $\mbox{Observer #2} = 1 \; \mbox{meter tall}$
• $\mbox{Meters from Observer #1} = 2$
• $\mbox{Meters from church} = 90$

Question:

• $\mbox{How tall is the church?}$

Rationale:

• $\mbox{We have two similar triangles one within the other.}$
• $\mbox{A small one: 1 meters vertical by  2 meters horizontal describing an angle} = \theta$
• $\mbox{A large one: the height of church vertical by 92 meters horizontal  describing an angle} = \theta$
• $\dfrac{vertical_{small}}{horizontal_{small}} = \tan\theta$
• $\dfrac{vertical_{church}}{horizontal_{church}} = \tan\theta$

Calculate:

• $\tan\theta = \dfrac{1}{2} \; \mbox{using the small triangle}$
• $\dfrac{vertical_{church}}{horizontal_{church}} = \tan\theta$
• $\dfrac{vertical_{church}}{92} = \tan\theta = 0.5$
• $vertical_{church} = 0.5 * 92 = 46 \; \mbox{meters}$

References:

• Similar Triangles