a chimney of 20m height standing on the top of a building subtends an angle whose tangent is 1/6 at a distance of 70m from the foot of the building find the height of the building .
To find the height of the building, we can solve this problem using trigonometry.
Let's call the height of the building "x". We know the height of the chimney is 20m.
Based on the given information, we can set up the following equation:
tan(θ) = opposite/adjacent
In this case, the opposite side is the height of the chimney (20m), and the adjacent side is the distance from the foot of the building to the point where the angle is being measured (70m + x).
So, we have:
tan(θ) = 20 / (70 + x)
Since we know that the tangent of the angle is 1/6, we can substitute this into the equation:
1/6 = 20 / (70 + x)
Now, we can solve for x:
Cross multiplying, we get:
20 = (70 + x) / 6
Multiply both sides by 6:
120 = 70 + x
Subtracting 70 from both sides:
x = 120 - 70
x = 50
Therefore, the height of the building is 50 meters.
To find the height of the building, we can use basic trigonometry. Let's break down the problem step by step:
1. Draw a diagram: Sketch a right triangle representing the situation described. Label the height of the chimney as "h" and the distance from the foot of the building to the point where the angle is subtended as "x."
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h | \
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----|---\
x | \
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2. Determine the tangent of the angle: Since the tangent of the angle is given as 1/6, we have:
tan(angle) = 1/6
3. Use the tangent formula: The tangent of an angle in a right triangle is equal to the ratio of the side opposite the angle to the side adjacent to the angle. In our case, the opposite side is h and the adjacent side is x, so we can write:
tan(angle) = h / x
4. Substitute the values: Substituting the known values into the equation, we have:
1/6 = h / x
5. Rearrange the equation: To solve for h, we can rearrange the equation to isolate h:
h = (1/6) * x
6. Substitute the values: We are given that x = 70m, so substituting this value into the equation, we have:
h = (1/6) * 70
7. Simplify the expression: Evaluating the expression, we have:
h = 70/6
8. Simplify the fraction: To simplify the fraction, divide the numerator by the denominator:
h = 11.67m
Therefore, the height of the building is approximately 11.67 meters.
(20 + height)/70 = tanØ = 1/6
120 + 6height = 70
6 height = -50
height can't be negative
Check your typing, the question makes no sense
(I read it that the tan of the subtended angle is 1/6)