Question
Find the person height.
- 4 ft
- 6.25 ft
- 1.25 ft
- 5.75 ft
Hint:
We are given a figure with a tree and a man forming a triangle with one point and the ground. We are given the height of the tree. We are also given the values of the distance of the tree and man from the point. We are asked to find the value of the man’s height. Both the triangles are right-angled triangles. So, we will its properties to solve the question.
The correct answer is: 6.25 ft
Both the man and tree forms a triangle.
Let the triangle formed by the person be ∆ABC and the triangle formed by the tree be ∆PQR.
From the figure,
BC = 5ft
PQ = 25ft
QR = 20ft
The height of the man is denoted by h.
We have to find the height of the man i.e. side AB
The ∠ABC and ∠PQR is equal to 90°. As the height of the person and the tree is perpendicular to the ground.
From the figure, we can see that the ∠B and ∠Q is same. It is a common angle to both of the triangles.
∠ACB = ∠PRQ
So, by AA test both the triangles are similar.
∆ABC ~ ∆PQR
Similar triangles have same shape but different size. Their sides are in proportion to each other. The ratio of their sides is equal.
Using the properties of similar triangle we can find the height of the tree.
Taking the ratios
Therefore, the height of the person is 4ft.
For such questions, we should know the properties of both right angled triangles and similar triangles. We should know about different tests to see if the triangles are similar or not.
Related Questions to study
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For such questions, we should know the properties of the similar objects.
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ByTo find the height of a very tall pine tree, you place a mirror on the ground and stand where you can see the top of the pine tree. Find the tree tall .
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You are making a guitar pick that resembles an equilateral triangle with side lengths of 32 millimeters. The approximate height of the pick is?
For such questions, the properties of right-angled triangles are important. We should know about the trigonometric ratios. It includes sine, cosine, tangent etc.
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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.
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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.
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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.
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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.
