Q8 of 68 Page 9

In AABC, hypotenuse AC = 12 cm and ∠A = 60°, then find the length of remaining sides.

Drawing the triangle for better reference of the problem.



Here we are actually sure that B is the 90 degrees angle as the ends of the hypotenuse can never have 90 degrees.


Also, when the ends are produced backwards (where angle A is produced backwards at an angle of 60 degrees) they seem to form a 90 degree angle.


The remaining sides length can be figured out by simple trigonometry,


Using



⇒


or, AB = 6cm.


Now, using


⇒


or, BC=


= 6√3 cm.


More from this chapter

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6

ABC is a right triangle in which BC is horizontal, AB = 8 m, ∠BAC = 60°, then find

(i) the angle of elevation of A at C


(ii) the angle of depression of C at A


(iii) the distance of B from C

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In the figure PQR is a right triangle in which and ∠QPR = 30°. Find QP.

 9

In right angled triangle ABC, AC is the hypotenuse, AB = 12 cm and ∠ BAC = 30˚, then find the length of the side BC.

 10

The top of a tower makes an angle of 45° at a point in the horizontal plane at a distance of 20 m. Find the height of the tower.