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Heights and Distances

Heights and Distances: Formulas, Shortcuts and Solved Examples

Heights and distances turn a real tower, ladder or river into a right-angled triangle. This lesson…
A pole is 35 metres tall and its shadow is also 35 metres long. Find the angle of elevation of the sun.
What is the value of tan(30 degrees)?
What is the value of tan(60 degrees)?
What is the value of tan(45 degrees)?
In a right triangle, what is the correct formula for the tangent of an angle theta?
When a person looks down at an object below the level of their eye, the angle the line of sight makes with the horizontal is called what?
When a person looks up at an object above the level of their eye, the angle the line of sight makes with the horizontal is called what?
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 78 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 52 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 44 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 102 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 70 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 26 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 16 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 72 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 10 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60 degrees. When he retires 36 m from the bank, he finds the angle of elevation to be 30 degrees. Find the breadth of the river.
The angle of elevation of the top of a tower at a point on the ground is 30 degrees. On walking 26 m towards the tower, the angle of elevation becomes 60 degrees. Find the height of the tower.
The angle of elevation of the top of a tower at a point on the ground is 30 degrees. On walking 30 m towards the tower, the angle of elevation becomes 60 degrees. Find the height of the tower.
The angle of elevation of the top of a tower at a point on the ground is 30 degrees. On walking 34 m towards the tower, the angle of elevation becomes 60 degrees. Find the height of the tower.
The angle of elevation of the top of a tower at a point on the ground is 30 degrees. On walking 54 m towards the tower, the angle of elevation becomes 60 degrees. Find the height of the tower.
The angle of elevation of the top of a tower at a point on the ground is 30 degrees. On walking 68 m towards the tower, the angle of elevation becomes 60 degrees. Find the height of the tower.
The angle of elevation of the top of a tower at a point on the ground is 30 degrees. On walking 4 m towards the tower, the angle of elevation becomes 60 degrees. Find the height of the tower.
The angle of elevation of the top of a tower at a point on the ground is 30 degrees. On walking 38 m towards the tower, the angle of elevation becomes 60 degrees. Find the height of the tower.

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