A woman who is 5 feet 5 inches tall is standing near the space needle in Washington; she casts a 13 inch shadow at the same time that the space needle casts a 121-foot shadow. How tall is the space needle?
+26400 A woman who is 5 feet 5 inches tall is standing near the space needle in Washington; she casts a 13 inch shadow at the same time that the space needle casts a 121-foot shadow. How tall is the space needle ?
intercept theorem:
$$\\ \small{\text{$
\\ \dfrac{h}{121\;\rm{foot} } = \dfrac{ 5\;\rm{foot}+5\;\rm{inch} }{13\;\rm{inch} } $}}\\ \\
\small{\text{$
\dfrac{h}{121\;\rm{foot} } = \dfrac{ 60\;\rm{inch}+5\;\rm{inch} }{13\;\rm{inch} } $}}\\ \\
\dfrac{h}{121\;\rm{foot} } = \dfrac{ 65\;\rm{inch} }{13\;\rm{inch} } $}}\\ \\
\dfrac{h}{121\;\rm{foot} } = \dfrac{ 65\;\not{\rm{inch}} }{13\;\not{\rm{inch}} } $}}\\ \\
\dfrac{h}{121\;\rm{foot} } = \dfrac{ 65 }{ 13 } $}}\\ \\
h= 121 \cdot \dfrac{ 65 }{ 13 } \;\rm{foot} $}}\\ \\
h= 605 \;\rm{foot} $}}$$
The space needle is 605 feet tall.
+26400 A woman who is 5 feet 5 inches tall is standing near the space needle in Washington; she casts a 13 inch shadow at the same time that the space needle casts a 121-foot shadow. How tall is the space needle ?
intercept theorem:
$$\\ \small{\text{$
\\ \dfrac{h}{121\;\rm{foot} } = \dfrac{ 5\;\rm{foot}+5\;\rm{inch} }{13\;\rm{inch} } $}}\\ \\
\small{\text{$
\dfrac{h}{121\;\rm{foot} } = \dfrac{ 60\;\rm{inch}+5\;\rm{inch} }{13\;\rm{inch} } $}}\\ \\
\dfrac{h}{121\;\rm{foot} } = \dfrac{ 65\;\rm{inch} }{13\;\rm{inch} } $}}\\ \\
\dfrac{h}{121\;\rm{foot} } = \dfrac{ 65\;\not{\rm{inch}} }{13\;\not{\rm{inch}} } $}}\\ \\
\dfrac{h}{121\;\rm{foot} } = \dfrac{ 65 }{ 13 } $}}\\ \\
h= 121 \cdot \dfrac{ 65 }{ 13 } \;\rm{foot} $}}\\ \\
h= 605 \;\rm{foot} $}}$$
The space needle is 605 feet tall.
