Mathematics
Grade9
Easy

Question

Find the person height.

  1. 4 ft
  2. 6.25 ft
  3. 1.25 ft
  4. 5.75 ft

hintHint:

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 
    fraction numerator A B over denominator P Q end fraction equals space fraction numerator B C over denominator Q R end fraction
h over 20 equals 5 over 25
h space equals space fraction numerator 20 cross times 5 over denominator 25 end fraction
h space equals space 4 f t
    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.

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