Question

In a right triangle ABC, right angled at C, if ∠B= 60° and AB = 15 units. Find the remaining angles and sides.

Answer 1

Answer:

60° angle is acute because it is less than 90

Answer 2

∠A = 30°, ∠B = 60° and ∠C = 90°.

AB = 15 units, BC = 7.5 units and AC = 13 units.

Step-by-step explanation:

Given: In a right triangle ABC, right angled at C, if ∠B= 60° and AB = 15 units

Find: remaining angles and sides.

Solution:  

 Sum of all angles in a triangle = 180°.

 ∠B = 60° and ∠C = 90°

 Therefore ∠A = 180° - (90° + 60°) = 30°

 Since C is 90°, AB will be the hypotenuse.

 AB = 15 units.

 Sin A = Opposite/Hypotenuse

 Sin 30° = BC / AB

  1/2 = BC / 15

  BC = 15/2 = 7.5 units.

 Cos A = Adjacent / Hypotenuse

  Cos 30° = AC / AB

 √3 / 2 = AC/ 15

 AC = 15√3/2 = 12.975 units or approximately 13 units.

 So the angles are ∠A = 30°, ∠B = 60° and ∠C = 90°.

 So the sides are AB = 15 units, BC = 7.5 units and AC = 13 units.