Solution - Pythagoras Theorem

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ConceptPythagoras Theorem

Question

A ladder leaning against a wall makes an angle of 60° with the horizontal. If the foot of the ladder is 2.5 m away from the wall, find the length of the ladder

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Nazima is fly fishing in a stream. The tip of her fishing rod is 1.8 m above the surface of the water and the fly at the end of the string rests on the water 3.6 m away and 2.4 m from a point directly under the tip of the rod. Assuming that her string (from the tip of her rod to the fly) is taut, ho much string does she have out (see Figure)? If she pulls in the string at the rate of 5 cm per second, what will be the horizontal distance of the fly from her after 12 seconds?

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ABC is a right-angled triangle, right-angled at A. A circle is inscribed in it. The lengths of the two sides containing the right angle are 5 cm and 12 cm. Find the radius of the circle

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ABCD is a rectangle whose three vertices are B (4, 0), C(4, 3) and D(0,3). The length of one of its diagonals is
(A) 5
(B) 4
(C) 3
(D) 25

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ABC is an isosceles triangle with AC = BC. If AB2 = 2AC2, prove that ABC is a right triangle.

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In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:

1)AC^2 = AD^2 + BC . DM + ((BC)/2)^2

2) AB^2 = AD^2 – BC . DM + ((BC)/2)^2

3) AC^2 + AB^2 = 2 AD^2 + 1/2(BC)^2

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Reference Material

Solution for concept: Pythagoras Theorem. For the course 8th-10th CBSE
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