Question

A tree broke at a point but did not form two pieces. Its top touched the ground
at a distance of 8ft from its base. If the point where it broke was at a height of
15ft from the ground, What was the total height of the tree before breaking?

Answer 1

$\large\underline{\bold{Solution-}}$

Let us suppose that the total height tree, AB be 'h' meter.

Let at point C, a tree AB broke and it top touches the ground at D.

• So, Height of the tree, AB = AC + CB

Since, BC touches the ground at D

• So, BC = CD

According to given statement,

• AC = 15 feet.

• AD = 8 feet.

So,

By pythagoras theorem,

• ⇛ CD² = AC² + AD²

• ⇛ CD² = (15)² + (8)²

• ⇛ CD² = 225 + 64

• ⇛ CD² = 289

• ⇛ CD = 17 feet

So,

• BC = CD = 17 feet

Hence,

• Height of tree, AB = AC + BC = 15 + 17 = 32 feet.

Additional Information

Properties of a triangle

• A triangle has three sides, three angles, and three vertices.

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Based on the angle measurement, there are three types of triangles:

• Acute Angled Triangle : A triangle that has all three angles less than 90° is an acute angle triangle.

• Right-Angled Triangle : A triangle that has one angle that measures exactly 90° is a right-angle triangle.

• Obtuse Angled Triangle : triangle that has one angle that measures more than 90° is an obtuse angle triangle.

Answer 2

Answer:

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