Step-by-step explanation:
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A streetlight that is 9 feet tall casts a 2-foot-long shadow. A nearby flagpole casts a 11-foot-long shadow. What is the height
1 answer:
The height of flagpole is 49.5 feet.
Step-by-step explanation:
Given,
Shadow casted by streetlight = 2 foot
Height of streetlight = 9 feet
Ratio of shadow to height = 2:9
Shadow casted by flagpole = 11 foot
Let,
x be the height of flagpole
Ratio of shadow to height = 11:x
Using proportion
Ratio of shadow to height :: Ratio of shadow to height
Product of mean = Product of extreme
Dividing both sides by 2
The height of flagpole is 49.5 feet.
Keywords: ratio, proportion
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I draw the two triangles, see the picture attached.
As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.
Angles <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>
Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles.
BAQ = QRP because they are alternate interior angles.
Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.
As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.
Angles <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>
Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles.
BAQ = QRP because they are alternate interior angles.
Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.