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

2 Answers
Alan P.
Jun 16, 2015

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

Meave60
Jun 16, 2015

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:

![https://en.wikipedia.org/wiki/Right_triangle](useruploads.socratic.org)

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

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