Question

23. Find the height of a tree, if it casts a shadow 15 m long on the level of ground, when the

angle of elevation of the sun is 450 .

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Answer 1

Answer:

✪SOLUTION✪

To solve these type of Questions we have to assume something.

From the attached figure, we have assumed that:

• OX is ground level.
• AB is height of the tower.
• BC is casted shadow by tower AB
• ∠ABC=90°
• ∠ACB=45° (Angle of elevation)

We have to find height of the tower i.e AB.

Since:

∠ABC=90°, therefore, ∆ABC is right angled at B

Now:

In right ∆ABC, we have:-

• AB= perpendicular (p)
• BC= base (b)
• AC= hypotenuse (h)

As we know:

$= > tanθ = \frac {p}{b} where \:θ = {45}^{0}$

$= > tan {45}^{0} = \frac{p}{15}$

☞tan45°=1

$= > 1 = \frac{p}{15}$

$= > p = 15$

Hence perpendicular (p) which is height of the tower is 15cm.

Another shortcut method:

If angle of elevation is 45° then the value of perpendicular and base are same.

• Here, length of shadow is 15cm and angle of elevation is 45°, therefore, height will also be 15cm.

If it helps you plz make it as brainliest and try to thank it too❤️

@Avishek91