Can someone plz help me?
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The triangles are proportional. There is the small triangle (5 ft, 6 ft, hypotenuse). There is the larger triangle that includes the small triangle (30 ft, height).
That means the side lengths are proportional.
#5/h=6/(30+6) rarr# The side lengths of the small triangle over the side lengths of the large triangle, with #h# representing the unknown height.
Now, let's solve the proportion:
#5/h=6/30 rarr# Simplify the second fraction
#5/h=1/5 rarr# Cross multiply (multiply the h by 1, the 5 by 6) and set the products equal to each other
#h=5*5#
#h=25 rarr# This is the height
The height of the statue (#h#) is #25# feet.
Since the smaller triangle and the larger triangle are similar, we can set up a proportion between them.
Sometimes it is easier to say it out loud in English first:
#"The ratio of the distance from the right point to the person (6 ft.) and the person's height (5 ft.)"#
#"is proportional to"#
#"the ratio of the distance from the right point to the statue (30 ft.) and the statue's height (h ft.)."#
Now write down that proportion in math and solve for #h#:
#(6" ft")/(5" ft")=(30" ft")/(h" ft")#
#(6color(red)cancelcolor(black)"ft")/(5color(red)cancelcolor(black)"ft")=(30color(red)cancelcolor(black)"ft")/(hcolor(red)cancelcolor(black)"ft")#
#6/5=30/h#
Cross-multiply:
#6h=30*5#
#6h=150#
#h=150/6#
#h=25#
That's the answer. Hope this helped!
assume the height of the statue is h and set a proportion:
(height of the man / length of his shadow) = (height of the statue/ length of its shadow)
# (5ft) / (6ft) = h/ (30ft) #
then cross multiply
30ft # * #5ft = h ft #*# 6ft
so, # 150ft = 6h ft#
# H= (150 / 6) ft #
#H= 25 ft#
