# From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 2.5 m from the banks, find the width of the river. [Take √3 = 1.732.

In the above figure, let XY be the bridge and A be the point on the bridge from which two points, say B and D, on opposite sides of the river are observed. Join B and C. Given that the angles of depression of B and C from the point A are 30° and 45° respectively. Join B, D to A. So, XAB = ABD = 30° and also YAD = ADB = 45°. Again, draw a line AC from A perpendicular to the ground. Then, we get two right-angled triangles ABC and ACD with right angles at C. Now, given that the height of the bridge is AC = 2.5 m. We have to find the width of the river, that is BD.

From ∆ACD,

CD = 2.5m.

Again from ∆ABC,

or,

Hence, the width of the river is BD = BC + CD = 4.33 + 2.5 = 6.83m, which is the required solution.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Heights and Distances33 mins
Quiz | Imp. Qs. on Heights and Distances37 mins
NCERT | Basics of Heights and Distances37 mins
Idioms and Phrases43 mins
Goprep Genius Quiz | Analogy and Classification48 mins
Acid - Types and Nomenclature52 mins
Agriculture and its Importance35 mins
Foundation | Permutation and Combination45 mins
Goprep Genius Quiz | Direction and Distance58 mins
Light and it's Reflection58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses