(1) From the information given in the figure,find the value of a and a

1.	(1) From the information given in the figure,find the value of a and also sides AC and BC.3x2x
Answer» Sum of angles in triangle 3x + 2x + x = 180° 6x = 180° x = 180°/6 = 30° x = 30° So, angle A = 3 × 30° = 90° angle B = 2 × 30° = 60° AB = 5 cm tan (B) = tan(60°) = AC/AB √3 = AC / 5 AC = 5√3 cmSimilarly, sin(B) = sin(60°) = AB/BC √3/2 = 5 cm/ BC BC = 10/√3 cm

(1) From the information given in the figure,find the value of a and also sides AC and BC.3x2x

Answer»

Sum of angles in triangle

3x + 2x + x = 180°

6x = 180°

x = 180°/6 = 30°

x = 30°

So, angle A = 3 × 30° = 90°

angle B = 2 × 30° = 60°

AB = 5 cm

tan (B) = tan(60°) = AC/AB

√3 = AC / 5

AC = 5√3 cmSimilarly,

sin(B) = sin(60°) = AB/BC

√3/2 = 5 cm/ BC

BC = 10/√3 cm