The lamp post is 800 cm high
From the diagram in the attachment below,
The height of the girl is /AG/ = 160cm
The length of her shadow is /SG/ = 90cm
The height of the lamp post is /LP/ = /LM/ + /MP/ = x + 160cm
To determine the height of the lamp post, we will calculate the value of x
Consider ΔASG
Determine <ASG = θ
From
[tex]tan\theta = \frac{opposite}{adjacent}[/tex]
Opposite = /AG/ = 160 cm
Adjacent = /SG/ = 90 cm
∴ [tex]tan\theta = \frac{160}{90}[/tex]
Also, Consider ΔLAM
[tex]tan\theta = \frac{/LM/}{/AM/}[/tex]
NOTE: <LAM = θ (Corresponding angles) since line AM is parallel to line SP
∴[tex]\frac{160}{90} = \frac{/LM/}{/AM/}[/tex]
But, /LM/ = x and /AM/ = 360 cm
∴[tex]\frac{160}{90} = \frac{x}{360}[/tex]
[tex]90x = 360 \times 160[/tex]
[tex]x = \frac{360 \times 160}{90}[/tex]
[tex]x = 4 \times 160 \\[/tex]
[tex]x = 640 cm[/tex]
x = 640 cm
Recall that, the height of the lamp post is /LP/ = /LM/ + /MP/ = x + 160cm
∴ The height of the lamp post is 640 cm + 160cm
The height of the lamp post is 800 cm
Hence, the lamp post is 800 cm high
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