Question

How do you solve the right triangle given A = 59°, a = 13, b = 14 ?

Answer 1

The given values are not those of a right triangle.

Explanation:

If `/_A = 59^@` and side `a` (the side opposite `/_A`) has a length of `13`

then the adjacent side has a length:
`color(white)("XXXX")` `"cotan"(59^@)*13 = 7.811`
and the hypotenuse has a length:
`color(white)("XXXX")` `"cosecant"(59^@)*13 = 15.166`

Neither of these matches the side given as `b=14`

Answer 2

Subtract angles A and C from `180^"o"` to find the missing angle B. Use the Pythagorean theorem to find side c, which is the hypotenuse. Angle B is `31^"o"` and the hypotenuse is 19.10#.

Explanation:

Angles
The angles of any triangle add up to `180^"o"`. We know that angle C is `90^"o"` (the right angle), and the other angle A is `59^"o"`. So we can determine angle B by adding angles A and C together, and subtracting the result from `180^"o"`

Angle B: `180^"o"-(90^"o"+59^"o")=31^"o"`

Angle B = `31^"o"`

Sides
You have been given side a =13 and side b = 14, so you need to find side c, which is the hypotenuse. Use the Pythagorean theorem to do this.

`c^2=a^2+b^2` =

`c^2=13^2+14^2` =

`c^2=365`

`c=sqrt(365)=19.10`

`c="hypothenuse"=19.10`