Question

In ΔABC, ∠C is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.

b= 20, c=40

Answer 1

The remaining side and angles are
`a = 20√(3)`,
`\angle A = 60^(\circ)` and
`\angle B = 30^(\circ)`.

Explanation:

According to the information given on statement, we are in front of a right triangle because
`\angle C`, opossite to side
`c`, is a right angle. Hence,
`c` is the hypotenuse of the right triangle and
`b`, a leg. The missing length can be calculated by the Pythagorean Theorem:

`a = \sqrt{c^(2)-b^(2)}` (1)

If we know that
`c = 40` and
`b = 20`, then the length of the missing leg is:

`a = \sqrt{c^(2)-b^(2)}`

`a = 20√(3)`

Lastly, we find the value of the missing angles by means of direct and inverse trigonometric relations:

Angle A

`\angle A = \tan^(-1)\left((a)/(b) \right)` (2)

Angle B

`\angle B = \tan^(-1) \left((b)/(a) \right)` (3)

If we know that
`a = 20√(3)` and
`b = 20`, then the values of the missing angles are, respectively:

Angle A

`\angle A = \tan^(-1)\left((a)/(b) \right)`

`\angle A = 60^(\circ)`

Angle B

`\angle B = \tan^(-1) \left((b)/(a) \right)`

`\angle B = 30^(\circ)`

The remaining side and angles are
`a = 20√(3)`,
`\angle A = 60^(\circ)` and
`\angle B = 30^(\circ)`.