Q16 of 27 Page 289

In ΔABC, if AB = (2a-1)cm. AC = 2 √2acm. And BC = (2a + 1)cm., then let us write the value of ∠BAC.


Let’s consider that the triangle is a right angled triangle,


By applying Pythagoras theorem we get,


(2a + 1)2 = (2√2a)2 + (2a-1)2


⇒ (2a)2 + 12 + 2×2a×1 = 4×2a + (2a)2 + 12 - 2×2a×1


⇒ 4a2 + 1 + 4a = 8a + 4a2 + 1 - 4a


⇒ 4a2 + 1 + 4a = 4a2 + 1 + 4a


Since, the sides of the triangle satisfy Pythagoras theorem, thus the triangle is a right angled triangle with angle opposite to hypotenuse as right angle.


Here,


H = 2a + 1


P = 2a-1


B = 2√2a


Thus, ∠BAC is a right angle with measure 90°.


More from this chapter

All 27 →
15

Let us write whether the following statements are true or false:

(i) If the ratio of the lengths of three sides of a triangle is 3:4:5, then the triangle will always be a right angled triangle.


(ii) If in a circle of radius 10cm. length, a chord subtends right angle at the centre, then the length of the chord will be 5cm.

 15

Let us fill in blanks:

(i) In a right angled triangle, the area of square drawn on the hypotenuse is equal to the _______of the areas of the squares drawn on other two sides.


(ii) In an isosceles right-angled triangle if the length of each of two equal sides is 42cm., then the length of the hypotenuse will be _______cm.


(iii) In a rectangular figure ABCD, the two diagonals AC and BD intersect each other at the point O, if AB = 12 cm., AO = 6.5 cm., then the length of BC is _______cm.

 16

In the adjoining figure, the point O is situated within the triangle PQR in such a way that ∠POQ = 90°, OP = 6cm. and OQ = 8cm. If PR = 24cm. and ∠QPR = 90°, then let us write the length of QR.

 16

The point O is situated within the rectangular figure ABCD in such a way that OB = 6 cm., OD = 8cm. and OA = 5cm. Let us determine the length of OC.