Question

A flag pole is 8cm tall Casts 10m shadow. at the same time ,a nearby building casts a shadow of 30 m how tall is the building
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Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Height\:of\:building=24 m}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ : \implies \: \text{Length \: of \: pole = 8 m} \\ \\ : \implies \text{Shadow \: of \: pole = 10 m} \\ \\ : \implies \text{Shadow \: of \: building = 30 m} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Height \: of \: building = ?}$

• In the given question the angle of depression of sunlight to both the pole and building is same.

• According to given quetion :

$\text{In \: right} \: \triangle \text{ABC}\\ : \implies tan \: \theta = \frac{p}{b} \\ \\ : \implies tan \: \theta = \frac{AB}{BC} \\ \\ : \implies tan \: \theta = \frac{8}{10}=\frac{4}{5} - - - - - (1) \\ \\ \text{In \: right} \: \triangle \: \text{DEF} \\ : \implies tan \: \theta = \frac{p}{b} \\ \\ :\implies tan \: \theta = \frac{DE}{EF}$$: \implies tan \: \theta = \frac{DE}{30} \\ \\ : \implies \frac{4}{5} = \frac{DE}{30} \\ \\ : \implies \frac{4 \times 30}{5} = de \\ \\ \green{: \implies \text{DE = 24 \: m}} \\ \\ \green{\therefore \text{Height \: of \: building = 24 \: m}}$

Answer 2

Question :-- A flag pole is 8m tall Casts 10m shadow. at the same time ,a nearby building casts a shadow of 30 m how tall is the building ?

Formula used :--

→ when Time is same angle of Elevation and Angle of Depression of sun will be same all over ...

→ Tan@ = Perpendicular/Base

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Solution :---

✪✪ Case 1 ✪✪

❁❁ Refer To Image First .. ❁❁

in ∆ABC , we have ,

→ AB = Flag Pole = 8m

→ BC = shadow of Flag Pole = 10m .

→ Angle ACB = @

From this we get,

→ Tan@ = Perpendicular/Base = AB/BC = 8/10 = 4/5 ------------- Equation (1)

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✪✪ Case 2 ✪✪

❁❁ Refer To Image First .. ❁❁

in ∆DEF , we have ,

→ DE = Building = Let h m.

→ EF = shadow of Building = 30m .

→ Angle ACB = @ { as Time is same }.

From this we get,

→ Tan@ = Perpendicular/Base = DE/EF = h/30 ----------------- Equation (2)

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Putting value of Tan@ From Equation (1) in Equation (2) now , we get,

→ 4/5 = h/30

cross- Multiplying we get,

→ 4*30 = 5*h

→ 120 = 5h

Dividing both sides by 5 we get,

→ h = 24m .

Hence, Height of Building will be 24m at the same Time..

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since, Time is same in both case, we can do this in simple way also ,, { or we can say Time is constant .}

→ when shadow is 10m, Height is = 8m

→ when shadow is 1m, Height is = (8/10)m

→ when shadow is 30m , Height is = (8/10) * 30 = 24m.

So,, Height of Building will be 24m at the same Time..