One sees the top of a tree on a bank of a river at an elevation of $70^{\circ}$ from the other bank. Stepping 20 m back, he sees the top of the tree at an elevation of $55^{\circ}$ . If height of the person is $1.4 m$ then the width of river is $[t a n 70^{\circ} = 2.75, t a n 55^{\circ} = 1.43]$

26.4 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

21.66 m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

28.2 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

25.4 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
21.66 m

Let the width of river be AB = X and the person was standing initially at point C and step back 20 m to reach at D. Height CF of person being 1.4 m.

In Right -angled $△$ ABC

$t a n 70^{\circ} = \frac{A B}{A C} = \frac{A B}{x}$

$A B = x . t a n 70^{\circ} = x \times 2.75 = 2.75 x . . . (1)$

In Right -angled $△$ ABD

$t a n 55^{\circ} = \frac{A B}{A D} = \frac{A B}{(x + 20)}$

$A B = (x + 20) . T a n 55^{\circ} = 1.43 (x + 20) . . . (2)$

from 1 and 2 we have

$2.75 x = 1.43 (x + 20) 2.75 x = 1.43 x + 28.6 1.32 x = 28.6 x = 21.66 m Hence, the width of the river is 21.66 m$

Suggest Corrections

Similar questions

Q. A boy, 1.4 metres tall standing at the edge of a river bank sees the top of a tree on the edge of the other bank at an elevation of 55

^{o}

. Standing back by 3 metres, he sees it at an elevation of 45

^{o}

.
(a) Draw a rough figure showing these facts.
(b) How wide is the river and how tall is the tree?

[sin 55^{o} = 0.8192, cos 55^{o} = 0.5736, tan 55^{o} = 1.4281]

Q. An observer standing on a bank of river observes the top of a tree on the opposite bank making an angle of elevation

60^{\circ}

. He moves

30

m

backward and observes the top of the tree making an angle of elevation

30^{\circ}

. Find the height of the tree and the width of the river.

A tower is built on a river of width 80 m. One can see the top of the tower at an angle of elevation of $55^{\circ}$ and $65^{\circ}$ from either banks of the river. The height of tower measured from the water level is $[T a n 65^{\circ} = 2.14, T a n 55^{\circ} = 1.43]$

Join BYJU'S Learning Program

One sees the top of a tree on a bank of a river at an elevation of 70∘ from the other bank. Stepping 20 m back, he sees the top of the tree at an elevation of 55∘. If height of the person is 1.4 m then the width of river is [tan 70∘=2.75, tan 55∘=1.43]

One sees the top of a tree on a bank of a river at an elevation of $70^{\circ}$ from the other bank. Stepping 20 m back, he sees the top of the tree at an elevation of $55^{\circ}$ . If height of the person is $1.4 m$ then the width of river is $[t a n 70^{\circ} = 2.75, t a n 55^{\circ} = 1.43]$