A rock climber uses a rope to ascend a cliff. If the vertical height of the cliff is 35 meters and the rope makes an angle of 30° with the level ground, what is the minimum length of the rope required to reach the top?
70 m
The rope is the hypotenuse, vertical height is the opposite side, and the angle with the ground is 30°.
\(\sin 30° = \dfrac{\text{height}}{\text{rope length}} \Rightarrow \dfrac{1}{2} = \dfrac{35}{L}\)
\(L = 35 \times 2 = \mathbf{70 \text{ m}}\)
Similar Questions
A statue that is 1.6 metres in height is positioned on top of a pedestal. From a location on the ground, the angle of elevation to the top of the statue measures 60 degrees, while the angle of elevation to the top of the pedestal from the same point is 45 degrees. Determine the height of the pedestal.
A vertical pole of height H stands on the ground. From a point P on the ground, the angle of elevation of the top of the pole is 60°. From a different point Q, located 10 meters away from point P (directly along the line extending from the base of the pole), the angle of elevation to the top of the pole is 30°. What is the height of the pole?
A vertical pole TF has its base F on the ground. From a point A, 25 metres from F, the angle of elevation of T is x°. From another point B, 75 metres from F (and in the same line as A), the angle of elevation of T is y°. If the height of the pole is \(25\sqrt{{3}}\) metres, what is the value of x° + y°?
A tower is 20 meters tall. What is the length of the shadow cast by the tower when the sun's elevation is 45°?
A tower stands 50 metres tall. From its peak, the angles of depression to the top and bottom of a nearby building are measured as 30° and 45° respectively. Determine the approximate height of the building and the horizontal distance separating the tower from the building.
A tower generates a shadow that is 40 meters long when the sun's angle of elevation is 45 degrees. What is the height of the tower?
A wheelchair ramp needs to reach a platform that is 1.5 metres high. If the ramp is designed to make an angle of 30° with the level ground, what is the length of the ramp?
From a point A on the ground, the angle of elevation to the top of a building is 30°. From a point B, which is directly between A and the foot of the building, the angle of elevation is 60°. What is the ratio of the distance of point A from the building's foot to the distance of point B from the building's foot?
An airplane flying at a height of 300 m notices the angles of depression to two boats located on opposite sides as 45° and 30°. Find the distance between the two boats.
- A kite is soaring at an altitude of 75 meters above the ground, with its string temporarily secured to a point on the ground. The angle of elevation of the string relative to the ground is 30 degrees. Given that the string remains taut, what is the length of the string?
Important Questions from Heights and Distances
A peacock sitting at the top of a 3 meter high pole saw a snake approaching towards pole at a distance three times of the height of the pole. Then it jumping from pole will catch the snake at what distance from the pole if both are running with same speed ?
The foot of a ladder 25 m long is 7 m from the base of the building. If the top of the ladder slips by 4 m, then by how much distance will the foot of the ladder slide?
Two hotels stand 25 m apart. One of them is 70 m high and the angle of depression of the top of other as observed from the top of this hotel is 45°. Height of the other hotel is:
If the angles of elevation of a balloon from two consecutive kilometer-stones along a straight road are 30° and 60° respectively, then the height of the balloon above the ground will be:
The angle of elevation of the top of a tower from a point 20 m away from its base is 45 °. What is the height of the tower?
