Question

1) A 15 m long ladder reached a window 12 m high from the ground on placing it
against a wall at a distance ‘a’m. Find the distance of the foot of the ladder from
the wall.

2) A tree is broken at a height of 5 m from the ground and its top touches the
ground at a distance of 12 m from the base of the tree. Find the original height of
the tree.

3) Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

4) Which of the following cannot be the measure of three angles of a triangle?
(i) ∠A = 60°, ∠B = 60°, ∠C = 60° (ii) ∠A = 70°, ∠B = 20°, ∠C = 100°
(iii) ∠A = 90°, ∠B = 90°, ∠C = 90° (iv) ∠A = 72°, ∠B = 30°, ∠C = 78°

5) Find the measure of the third angle of a triangle:
(i) ∠A = 60°, ∠B = 60° (ii) ∠A = 70°, ∠B = 80°
(iii) ∠A = 90°, ∠B = 10° (iv) ∠A = 95°, ∠B = 25°
6) Which of the following can be the sides of a right angled triangle?
i) 2.5 cm, 2 cm 1.5 cm (ii) 4 cm, 4 cm , 5 cm.

Answer 1

Hi!

Here is the answer to your question.

The given situation can be represented as



Let the distance of the foot of the ladder from the wall be a m. I.e., BC = a m

Applying Pythagoras Theorem,

BC2 + AB2 = AC2    (Pythagoras Theorem)

⇒ a2 + (12)2 = (15 m)2

⇒ a2 = 225 – 144

⇒ a2 = 81

⇒ a = 9

 

Thus, the distance of the foot of the ladder from the wall is 9 m.

 

Cheers!

Answer 2

Ans of 1st question is 7