The measure of the angle of elevation from point A is θ.
In right triangle APQ,
tan θ =
θ = 33°41′.
Correct answer : (3)
The angle of elevation of the top of a hill from the foot of a tower is 62° and the angle of elevation of the top of the tower from the foot of the hill is 28°. If the tower is 40 ft high, then find the height of the hill.
Draw the diagram.
Let represent the height of the hill and let represent the distance between the hill and the tower.
In right triangle QPA,
tan 28° =
= = 75
In right triangle PAB, tan 62° =
= 75 tan 62° = 141
The height of the hill is 141 ft.
Correct answer : (1)
Tom and Sam are on either side of a tower of height meters.They measure the angle of elevation of the top of the tower as and respectively. Find the distance through which Tom and Sam are seperated. [Given = 160, = 50° and = 35°.]
Height of the pole is AB = = 160 meters, C and D are the positions of Tom and Sam as shown. [Draw the diagram for the given data.]
ACB = = 50° and ADB = = 35° [Write the angles of elevation of A from Tom, Sam.]
In the right triangle ADB, tan = tan 35° = [tan = .]
BD = » 228.571 meters [Substitute the value of tan 35° and find BD.]
In the right triangle ABC, tan = tan 50° = [tan = .]
BC = » 134.340 meters [Substitute the value of tan 50° and find BC.]
CD = CB + BD = 228.571 +134.340 » 363 m [Use CD = CB + BD to find CD.]
So, the distance between Tom and Sam is 363 m.
Correct answer : (4)
The angle of depression of the top of a tower of height meters from the top of another tower of height H meters is 25°. Find the horizontal distance between the two towers when = 93 and H = 125.
Height of the first tower is CD = = 93 meters, height of the second tower is AB = H = 125 meters as shown [Draw the diagram for the given data.]
Let the distance between the two towers, BC = ED = meters and the difference between the heights of the two towers, AE = meters
The angle of depression of D from A is = 25° [Write the angle of depression of D from A.]
ADE = = 25° [ ADE = as ADE, are alternate angles.]
In the right triangle ADE, tan ADE = tan 25° = = and hence = 0.46 [Substitute the value of tan 25° and find in terms of .]
= AE = AB - BE = 125 - 93 = 32 meters [From the figure AE = AB - BE = .]