Asked by Nancy
Solve the angle of elevation of the top of a tower from a point 42cm away from its base on level ground is 36degree find the height of the tower.
Answers
Answered by
Nancy
An arerial mast has a shadow 40cm long on level ground when the elevation of the sum is 70 degree . Calculate the height of the mast.
Answered by
Bot
To solve for the height of the tower, we can use trigonometry.
Let's consider a right triangle with the base representing the distance from the point to the tower, the height representing the height of the tower, and the hypotenuse representing the distance from the point to the top of the tower.
In the right triangle, the angle of elevation is 36 degrees. This means that the angle between the base and the hypotenuse is also 36 degrees.
Using trigonometry, we can use the tangent function to relate the angle of elevation with the height of the tower:
tan(36°) = height / distance
Rearranging the equation, we get:
height = tan(36°) * distance
Substituting the given values, we have:
height = tan(36°) * 42 cm
Calculating this, we find:
height ≈ 30.693 cm
Therefore, the height of the tower is approximately 30.693 cm.
Let's consider a right triangle with the base representing the distance from the point to the tower, the height representing the height of the tower, and the hypotenuse representing the distance from the point to the top of the tower.
In the right triangle, the angle of elevation is 36 degrees. This means that the angle between the base and the hypotenuse is also 36 degrees.
Using trigonometry, we can use the tangent function to relate the angle of elevation with the height of the tower:
tan(36°) = height / distance
Rearranging the equation, we get:
height = tan(36°) * distance
Substituting the given values, we have:
height = tan(36°) * 42 cm
Calculating this, we find:
height ≈ 30.693 cm
Therefore, the height of the tower is approximately 30.693 cm.
Answered by
Bot
To solve for the height of the mast, we can again use trigonometry.
Let's consider a right triangle with the height of the mast representing the height, the length of the shadow representing the base, and the angle of elevation representing the angle opposite the height.
In the right triangle, the angle of elevation is 70 degrees.
Using trigonometry, we can use the tangent function to relate the angle of elevation with the height of the mast:
tan(70°) = height / shadow length
Rearranging the equation, we get:
height = tan(70°) * shadow length
Substituting the given values, we have:
height = tan(70°) * 40 cm
Calculating this, we find:
height ≈ 106.27 cm
Therefore, the height of the mast is approximately 106.27 cm.
Let's consider a right triangle with the height of the mast representing the height, the length of the shadow representing the base, and the angle of elevation representing the angle opposite the height.
In the right triangle, the angle of elevation is 70 degrees.
Using trigonometry, we can use the tangent function to relate the angle of elevation with the height of the mast:
tan(70°) = height / shadow length
Rearranging the equation, we get:
height = tan(70°) * shadow length
Substituting the given values, we have:
height = tan(70°) * 40 cm
Calculating this, we find:
height ≈ 106.27 cm
Therefore, the height of the mast is approximately 106.27 cm.
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