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Kate stands 2 meters from a lamppost. She is 2.1 meters tall and casts a shadow 3 meters long in the light from the lamp. How tall is the lamppost? See diagram below.​

Kate stands 2 meters from a lamppost She is 21 meters tall and casts a shadow 3 meters long in the light from the lamp How tall is the lamppost See diagram belo class=

Respuesta :

xKelvin

Answer:

3.5 meters.

Step-by-step explanation:

Please refer to the attachment.

Since the two triangles share two congruent angles, by AA Similarity, the two triangles are similar.

Therefore, we can write the following proportion:

[tex]\frac{3}{5}=\frac{2.1}{x}[/tex]

To find the height of the lamppost x, we will simply have to solve for x.

So, let’s cross-multiply:

[tex]10.5=3x[/tex]

Divide both sides by 3:

[tex]x=10.5/3=3.5[/tex]

Hence, the height of the lamppost is 3.5 meters.

Ver imagen xKelvin

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