Question
A tree is broken by the wind but does not separate. If the point from where it breaks is 9m above the ground and its top touches the ground at a distance of 12m from its foot, find out the total height of the tree before it broke.
✓
Answer
Let $A B$ be the tree which broke at $D$ and its top $A$ touches the ground at $C$.
Their $B D=5 m$ and $B C=12 m$
Let $A D=x m$, then $C D=x m$
Now, in right $\triangle ABC$,
$C D^2=B D^2+B C^2$ (By Pythagoras Theorom)
$C D^2=(9)^2+(12)^2$
$\Rightarrow C D^2=81+144$
$\Rightarrow C D^2=225$
$\Rightarrow C D^2=(15)^2$
$CD =15 m$
$AD = x =15 m$
Height of the tree $A B=A D+B D=15+9=24 m$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A door of dimensions $3 m \times 2 m$ is on the wall of dimension $10 m \times 10 m$. Find the cost of painting the wall if rate of painting is Rs. 2.50 per square meter.
→Construct a $\triangle\text{ABC}$ in which AB = 3.8cm, $\angle\text{A}=60^\circ$ and AC = 5cm.
→Evaluate:
$-3+\frac{1}{8}+\frac{-2}{5}$
→$-3+\frac{1}{8}+\frac{-2}{5}$
Draw $\triangle\text{ABC}$ in which BC = 8cm, $\angle\text{B}=50^\circ$ and $\angle\text{A}=50^\circ.$
→Students of a certain school went for a picnic to a farm by bus. Here are some of their experiences. Say whether the quantities in each are in direct or in inverse proportion.
i. Each student paid Rs 60 for the expenses.
As there were 45 students,___rupees were collected.
Had there been 50 students,___rupees would have been collected.
The number of students and money collected are in___proportion.
i. Each student paid Rs 60 for the expenses.
As there were 45 students,___rupees were collected.
Had there been 50 students,___rupees would have been collected.
The number of students and money collected are in___proportion.
ii. The sweets shop near the school gave 90 laddoos for the picnic.
If 45 students go for the picnic, each will get___laddoos.
If 30 students go for the picnic, each will get___laddoos.
The number of students and that of laddoos each one gets are in___proportion.
iii. The farm is 120 km away from the school.
The bus went to the farm at a speed of 40 km per hour and took___hours.
On the return trip, the speed was 60 km per hour. Therefore, it took___hours.
The speed of the bus and the time it takes are in___proportion.
iv. The farmer picked 180 bors from his trees.
He gave them equally to 45 students. Each student got___bors.
Had there been 60 students, each would have got___bors.
The number of students and the number of bors each one gets are in___proportion.
The radius of a circle is 14 cm . Find the radius of the circle whose area is double of the area of the circle.
By selling 8 dozen pencils, a shopkeeper gains the selling price of one dozen pencils. Find his gain percent.
A coin is tossed 300 times and we get head : 136 times and tail : 164 times.
When a coin is tossed at random, What is the probability of getting (i) a head, (ii) a tail?
When a coin is tossed at random, What is the probability of getting (i) a head, (ii) a tail?
An exterior angle of a triangle is 100° and its interior opposite angles are equal to each other. Find the measure of each angle of the triangle.
| (a) |  |
(I) |  |
| (b) |  |
(II) |  |
| (c) |  |
(III) |  |
| (d) |  |
(IV) |  |