Question

The upper part of a tree is broken by wind and falls to the ground without being detached. If the top of the broken part
touches the ground at a distanceof 12 feet from the foot of the tree, calculate the height at which it is broken if the original height is 24 feet.​

Answer 1

Answer:

10th

Maths

Some Applications of Trigonometry

Heights and Distances

The upper part of a tree br...

MATHS

The upper part of a tree broken by wind falls to the ground without being detached. The top of the broken part touches the ground at an angle of 38

o

30

′

at a point 6 m from the foot of the tree. Calculate

(i) the height at which the tree is broken.

(ii) the original height of the tree correct to two decimal places.

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ANSWER

Consider

TR as the height of the tree,

TP as the broken part which touches the ground at a distance of 6m from the foot of the tree which makes an angle of 38

o

30

′

with the ground.

Take PR=x and PQ=PT=y

Thus, TR=x+y

In right triangle PQR,

tanθ=

QR

PR

Substituting the values,

⇒tan38

o

30

′

=

6

x

⇒0.7954=

6

x

⇒x=0.7954×6=4.7724

sinθ=

PQ

PR

Substituting the values,

⇒sin38

o

30

′

=

y

x

⇒0.6225=

y

4.7724

⇒y=

0.6225

4.7724

=7.6665

Hence,

Height of the tree =4.7724+7.6665=12.4389=12.44 m.

Height of the tree at which it is broken =4.77 m.

solution