Question

In right-angled triangle, the difference between two of the angles is 20 degrees. a) Work out the Size of the angles in the triangle. b) How many solutions are there to A? ​

Answer 1

The sum of interior angles of a triangle is 180°

In a right triangle, one of the three angles is 90°. Therefore, the sum of the other two angles is 90°.

Let a = one unknown angle

Let b = the other unknown angle

As the sum of the angles is 90°:

⇒ a + b = 90°

As the difference between the two angles is 20°:

⇒ a - b = 20°

Rewriting the first equation to make a the subject:

⇒ a = 90° - b

Substituting this into the second equation and solving for b:

⇒ 90° - b - b = 20°

⇒ 90° -2b = 20°

⇒ 70° = 2b

⇒ b = 35°

Substituting found value for b into a = 90° - b and solving for a:

⇒ a = 90° - 35°

⇒ a = 55°

Therefore, the two unknown angles are 35° and 55°