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CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, Canada. The tower includes a rotating restaurant high above the ground. From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c . (i) How tall is the CN Tower? (ii) How far below the pinnacle of the tower is the restaurant located?
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CN Tower : The tallest free-standing tower in the world is the CN Towe...
Solution:
(i) Height of the CN Tower
Let AB be the CN Tower and C be the point of observation. Let BC = x and AB = h.
From the given information, we have:
Angle of elevation of the top of the tower from point C = 60°
Angle of elevation of the restaurant from point C = 45°
In right triangle ABC, we have:
tan 60° = AB/BC
√3 = h/x
h = x√3
In right triangle ABD, we have:
tan 45° = BD/AD
1 = BD/(h - 208)
h - 208 = BD
BD = h - 208
Substituting the value of h from equation (1), we get:
BD = x√3 - 208
In right triangle ACD, we have:
tan 60° = AD/AC
√3 = AD/(x + BD)
√3(x + BD) = AD
Substituting the value of BD from equation (2), we get:
AD = √3(x√3 - 208 + x)
AD = x√3 + 3x - 208√3
In right triangle ABD, we have:
sin 45° = BD/AD
1/√2 = (x√3 - 208)/[x√3 + 3x - 208√3]
Solving for x, we get:
x = 450
Substituting the value of x in equation (1), we get:
h = x√3 = 450√3 ≈ 778 m
Therefore, the height of the CN Tower is approximately 778 m.
(ii) Height of the restaurant above the ground
Let AB be the CN Tower and C be the point of observation. Let BC = x and AB = h.
From the given information, we have:
Angle of elevation of the top of the tower from point C = 60°
Angle of elevation of the restaurant from point C = 45°
In right triangle ABD, we have:
tan 45° = BD/AD
1 = BD/(h - 208)
h - 208 = BD
BD = h - 208
In right triangle ACD, we have:
tan 45° = CD/AC
1 = CD/(x + BD)
x + BD = CD
Substituting the value of BD from equation (1), we get:
CD = x + h - 208
In right triangle ABC, we have:
tan 60° = AB/BC
√3 = h/x
x = h/√3
Substituting the value of x in equation (3), we get:
CD = h - 208 + h/√3
CD = h(1 + 1/√3) - 208
CD = 778(1 + 1/√3) - 208 ≈ 335 m
Therefore, the restaurant is located approximately 335 m below the pinnacle of the tower.
(i) Height of the CN Tower
Let AB be the CN Tower and C be the point of observation. Let BC = x and AB = h.
From the given information, we have:
Angle of elevation of the top of the tower from point C = 60°
Angle of elevation of the restaurant from point C = 45°
In right triangle ABC, we have:
tan 60° = AB/BC
√3 = h/x
h = x√3
In right triangle ABD, we have:
tan 45° = BD/AD
1 = BD/(h - 208)
h - 208 = BD
BD = h - 208
Substituting the value of h from equation (1), we get:
BD = x√3 - 208
In right triangle ACD, we have:
tan 60° = AD/AC
√3 = AD/(x + BD)
√3(x + BD) = AD
Substituting the value of BD from equation (2), we get:
AD = √3(x√3 - 208 + x)
AD = x√3 + 3x - 208√3
In right triangle ABD, we have:
sin 45° = BD/AD
1/√2 = (x√3 - 208)/[x√3 + 3x - 208√3]
Solving for x, we get:
x = 450
Substituting the value of x in equation (1), we get:
h = x√3 = 450√3 ≈ 778 m
Therefore, the height of the CN Tower is approximately 778 m.
(ii) Height of the restaurant above the ground
Let AB be the CN Tower and C be the point of observation. Let BC = x and AB = h.
From the given information, we have:
Angle of elevation of the top of the tower from point C = 60°
Angle of elevation of the restaurant from point C = 45°
In right triangle ABD, we have:
tan 45° = BD/AD
1 = BD/(h - 208)
h - 208 = BD
BD = h - 208
In right triangle ACD, we have:
tan 45° = CD/AC
1 = CD/(x + BD)
x + BD = CD
Substituting the value of BD from equation (1), we get:
CD = x + h - 208
In right triangle ABC, we have:
tan 60° = AB/BC
√3 = h/x
x = h/√3
Substituting the value of x in equation (3), we get:
CD = h - 208 + h/√3
CD = h(1 + 1/√3) - 208
CD = 778(1 + 1/√3) - 208 ≈ 335 m
Therefore, the restaurant is located approximately 335 m below the pinnacle of the tower.
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CN Tower : The tallest free-standing tower in the world is the CN Towe...
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CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, Canada. The tower includes a rotating restaurant high above the ground. From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c . (i) How tall is the CN Tower? (ii) How far below the pinnacle of the tower is the restaurant located?
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CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, Canada. The tower includes a rotating restaurant high above the ground. From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c . (i) How tall is the CN Tower? (ii) How far below the pinnacle of the tower is the restaurant located? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, Canada. The tower includes a rotating restaurant high above the ground. From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c . (i) How tall is the CN Tower? (ii) How far below the pinnacle of the tower is the restaurant located? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, Canada. The tower includes a rotating restaurant high above the ground. From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c . (i) How tall is the CN Tower? (ii) How far below the pinnacle of the tower is the restaurant located?.
CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, Canada. The tower includes a rotating restaurant high above the ground. From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c . (i) How tall is the CN Tower? (ii) How far below the pinnacle of the tower is the restaurant located? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, Canada. The tower includes a rotating restaurant high above the ground. From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c . (i) How tall is the CN Tower? (ii) How far below the pinnacle of the tower is the restaurant located? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for CN Tower : The tallest free-standing tower in the world is the CN Tower in Toronto, Canada. The tower includes a rotating restaurant high above the ground. From a distance of 208 meter the angle of elevation to the pinnacle of the tower is 60c . The angle of elevation to the restaurant from the same vantage point is 45c . (i) How tall is the CN Tower? (ii) How far below the pinnacle of the tower is the restaurant located?.
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