Question
A power pole 10 m tall casts a shadow 8 meters long, at the same time that a building nearby casts a shadow 14 m long. Find the building tall.
- 9 m
- 15.2 m
- 12 m
- 17.5 m
Hint:
We are given the height of a pole and length of the shadow formed by it. We are also given the length of shadow of the building. It is stated that the shadows are casts at the same time. As the shadows are at the same time, their angles will be same. If we joined the ends of the building and the pole with their shadows, triangles are formed.
The correct answer is: 17.5 m
We will join the ends of the building and the pole with the ends of their shadows. Because of this, two triangles are formed.
Both the triangles will be right-angled triangles. So, their one angle is same
The time when shadow is cast is same. Therefore, the angle at which shadow is cast is same.
Two angle of the triangles are same. By AA test both the triangles are similar.
Similar triangles have same shape or angles.They have different sizes. Their sides are in proportion.
The ratio of the sides of two similar triangles is same. So, ratio of the length of the building and pole is equal to ratio of their respective shadows.
Let the length of building be “x”.
Therefore, the length of the shadow of the 17.5 m
We should know about different properties of similar triangles. We have to be careful about which sides to choose for the ratio. We should also know about different similarity tests.
Related Questions to study
Find the length of the altitude of triangle PQR.
To solve such questions, we should know the properties of right-angled triangles and similar triangles. Similar triangles have different sizes, but are of same shape. Their sides are in different proportion, but their angles are same. As a shortcut, we can just remember the last step of the above expression.
Find the length of the altitude of triangle PQR.
To solve such questions, we should know the properties of right-angled triangles and similar triangles. Similar triangles have different sizes, but are of same shape. Their sides are in different proportion, but their angles are same. As a shortcut, we can just remember the last step of the above expression.
Find the value of y.
For such questions, we should know the properties of right-angled triangle. We should know the trignometric ratios. The values of different sines and cosines should be known.
Find the value of y.
For such questions, we should know the properties of right-angled triangle. We should know the trignometric ratios. The values of different sines and cosines should be known.
A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.
For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem. Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.
A square has side length 95. The length of the diagonal of the square is? Express your answer in simplest radical form.
For such questions, we should know the properties of the right-angled triangle. The other method to solve it will be 45°-45°-90° theorem. Due to diagonal, the triangle which is formed has the sides in proportion 1:1:√2. Therefore, the value of hypotenuse is given by √2 multiplied by the value of the side.
