Question

A stick 1 meter long casts a shadow 0.7 meters long. A building casts a shadow 22 meters long. How tall is the building (to 2 decimal places)

Answer 1

A stick 1 meter long casts a shadow 0.7 meters long,

A building casts a shadow 22 meters long.

According to the given statement,

Since the both the angle θ are equal because they are form in the same source if light

From the property of similar triangle;

If one of the acute angles of a right triangle is congruent to an acute angle of another right triangle, then by Angle-Angle Similarity the triangles are similar.

So, triangleAOB is similar to triangle PQR

Now, from the property of similar triangle;

The SAS rule states that two triangles are similar if the ratio of their corresponding two sides is equal.

Thus,

`(AO)/(PQ)=(OB)/(QR)=(BA)/(RP)`

Substitute the value of the side; as,

OB = 1, AO = 0.7m

PQ = 22, QR

`\begin{gathered} (AO)/(PQ)=(OB)/(QR)=(BA)/(RP) \\ (0.7)/(22)=(1)/(QR) \\ \text{Apply cross multiplication;} \\ 0.7QR=\text{ 1}*22 \\ QR=(22)/(0.7) \\ QR=\text{ 31.42 m} \end{gathered}`

So, the height of the building , QR = 31.42 m

Answer : 31.42 m

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