Question

A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45°.Find the height of the tree​

Answer 1

Step-by-step explanation:

In △ABC,

x

h

=tan60

∘

⇒h=xtan60

∘

....(!)

In △ABD,

x+20

h

=tan45

∘

∴

x+20

xtan60

∘

=tan45

∘

[From equation (1)]

⇒

3

x=1×(x+20)⇒

3

x=x+20

⇒1.73x−x=20

⇒x=

0.73

20

=27.39

Hence, height of tree =h=27.39×

3

=47.39 m.

Answer 2

15m

• The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle. One of the six fundamental functions in trigonometry is the tangent function.
• We are aware that an angle's cosine is equal to the ratio of the length of the adjacent side to the length of the hypotenuse side, whereas an angle's sine is equal to the length of the opposite side divided by the length of the hypotenuse side. The tangent function in trigonometry is used to determine the slope of a line between the origin and a point denoting the intersection of a right triangle's hypotenuse and altitude. However, the tangent indicates the slope of an object in both geometry and trigonometry.

Here, according to the given information,

A tree casts a shadow 15 m long on the level of ground.

Let h be the height of the tree.

Then,

$\frac{h}{15}=tan45=1$

Or, h = 15 m.

Hence, height of a tree is 15 m.

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