Problem 1 :
Find the height of a vertical cliff if the angle of elevation is 25° to the top from a point which is 235 m from the base of the cliff.
Solution:
Let x be the height of a vertical cliff.
So, height of the vertical cliff is 109.58 m.
Problem 2 :
What angle will a 5 m ladder make with a wall if it reaches 4.2 m up the wall?
Solution:
Problem 3 :
The angle of elevation to the top of a lighthouse 25 m above sea-level from a fishing boat is 6°. Calculate the horizontal distance of the boat from the lighthouse.
Solution:
So, horizontal distance of the boat from the lighthouse is 238.09 m.
Problem 4 :
The angle of elevation from point A on horizontal ground to the top of a 20 m high pole is 35°. A rope is attached from A to the top of the pole. Find the length of the rope.
Solution:
So, length of the rope is 34.90 m.
Problem 5 :
A rectangular gate has a diagonal strut of length 3 m and an angle between the diagonal and a side is 28°. Find the length of the longer side of the gate.
Solution:
Let x be the longer side and y be the shorter side.
In triangle ABC,
cos θ = Adjacent side / Hypotenuse
cos θ = AB/AC
cos 28 = x/3
x = 3 cos 28
x = 3(0.882)
x = 2.646
So, the length of longer side is 2.646 m.
Problem 6 :
From a vertical cliff 80 m above sea level, a fishing boat is observed at an angle of depression of 6°. How far out to sea is the boat?
Solution:
So, the distance of the boat to the cliff is 762 m.
Problem 7 :
A railway line goes up an incline of constant angle 4° over a horizontal distance of 4 km. How high is it above the horizontal at the end of the incline?
Solution:
= 0.279 × 1000
= 279 m
Problem 8 :
At the entrance to a building there is a ramp for wheelchair access. The length of the ramp is 5 metres, and it rises to a height of 0.6 metres. Find the angle θ that the ramp makes with the ground.
Solution :
Problem 9 :
The roof of a bus shelter is supported by a metal strut 2.5 m in length, attached to the back wall of the shelter at an angle of 40˚. Calculate how far below the roof of the shelter the strut is attached to the wall.
Solution :
Hypotenuse = 2.5 m
cos 𝜃 = adjacent side / hypotenuse
cos 40 = Adjacent side / 2.5
Adjacent side = 2.5 cos 40
= 2.5 (0.766)
= 1.92 m
Problem 10 :
The diagram alongside shows a goalpost which has snapped in two after being hit by lightning. The top of the post is now resting 15 m from its base at an angle of 25˚. Find the height of the goal post before it snapped.
Solution :
Height = Opposite side
tan 𝜃 = Opposite side/adjacent side
tan 25 = Opposite side / 15
Opposite side = 15 (tan 25)
= 6.99
Height of the goal post before it snapped = 15 + 6.99
= 21.99
Approximately 23 m.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM