From the top of a church spire 96 m high, the angles of depression of two vehicles on a road, at the same level as the base of the spire and on the same side of it are x° and y°, where tan x° = and tan y° = . Calculate the distance between the vehicles.

Question

KnowledgeBoat · Accepted Answer

Let AB be the height of church = 96 m. Hence, the angle of elevation of the first vehicle at position D to the top of the church is x° and that of the second vehicle at position C is y°. Considering right angled △ABD, we get Considering right angled △ABC, we get The distance between the vehicles = 672 m - 384 m = 288 m. Hence, distance between the vehicles is 288 m.

Mathematics

From the top of a church spire 96 m high, the angles of depression of two vehicles on a road, at the same level as the base of the spire and on the same side of it are x° and y°, where tan x° = and tan y° = . Calculate the distance between the vehicles.

Heights & Distances

Related Questions

An aeroplane at an altitude of 900 m finds that two ships are sailing towards it in the same direction. The angles of depression of the ships, as observed from the plane, are 60° and 30° respectively. Find the distance between the ships.

In the given figure, AB is a tower and two objects C and D are located on the ground on the same side of AB. When observed from the top B of the tower, their angles of depression are 45° and 60° respectively. Find the distance between the objects, if the height of the tower is 180 m.

Two men standing on the same side of a tower in a straight line with it, measure the angles of elevation of the top of the tower as 25° and 50° respectively. If the height of the tower is 70 m, find the distance between the two men.