Right Triangles MCQ Quiz in मल्याळम - Objective Question with Answer for Right Triangles - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

In a right triangle, the tangent of one acute angle is the reciprocal of the tangent of the other. Given , the reciprocal is . Therefore, . This reciprocal relationship holds because the sum of and must be .

The diagonal of a square with side length is given by the formula . For a square with side length inches, the diagonal is inches. Thus, option 4 is correct. Option 1 is incorrect as it provides the side length, not the diagonal. Option 2 is incorrect as it erroneously doubles the side length. Option 3 is incorrect as it represents a miscalculation.

Using the Pythagorean theorem , where is the hypotenuse, we substitute and . We have , which is . Solving for , , so inches. Option 2 is correct. Option 1 is incorrect as it represents a miscalculation. Option 3 is incorrect because it provides the length of the given leg. Option 4 is incorrect due to calculation errors.

In a right triangle with a angle, the side opposite the angle is half the hypotenuse. Since the hypotenuse is units, the opposite side is units. Thus, the correct answer is option 3, units.

In a triangle, the side opposite the angle is half the hypotenuse. Therefore, the length of the side opposite the angle is inches. Option 1 is correct. Option 2 is incorrect because it mistakenly suggests the opposite side is equal to the hypotenuse. Option 3 is incorrect as it is the length of the side opposite the angle. Option 4 is incorrect as it represents a miscalculation.

In a rectangle, the diagonal forms the hypotenuse of a right triangle with the length and width. Using the Pythagorean theorem, , where is the length. This becomes . Subtract from both sides to get . Taking the square root gives . Thus, the length of the garden is meters.

The Pythagorean theorem states that in a right triangle, , where is the hypotenuse. Here, and . We need to find . Substituting the known values, we have . This simplifies to . Solving for , we subtract from both sides, yielding . Taking the square root of both sides gives . Therefore, the length of the other leg is .

The diagonal forms a right triangle with the width and length of the pool. Using the Pythagorean theorem, , where is the length. This simplifies to . Subtract from both sides to get . Taking the square root gives . Therefore, the length of the pool is meters.

The ratio of the sides is , which is a common Pythagorean triplet. Let , , and be the sides. The longest side . Solving for , we get . The shortest side is . Therefore, the length of the shortest side is cm.

The ladder forms a right triangle with the wall and the ground. Using the Pythagorean theorem, where the height feet and the ladder feet are given, we need to find the base . The equation is . Simplifying, we have . Subtract from both sides to get . Taking the square root gives . Hence, the base of the ladder is feet from the wall.