Question

A triangle has sides A, B, and C. Sides A and B are of lengths `7` and `5`, respectively, and the angle between A and B is `(5pi)/8`. What is the length of side C?

Answer 1

`c = 10`

Explanation:

Well this is a very tricky one, i wish i can draw the Triangle to explain better, but with the theory i hope you will understand..

Firstly Note that the Angle is in Radians..

If you observe closely,

Angel between A and B is `color(white)(x)5pi/8`

You're aware that there are only 3 angels which are `A, B, C`

Now again; What is the Angle between `A and B` ?

Simple, the answer is `C`

Cause it's a Triangle so the angle is C, since it's in between the two angles..

It's just a trick to push you off course from the desired Answer..

Hence we have as follows;

`C^o = 5pi/8`

`a = 7`

`b = 5`

`c = ?`

Before we proceed further, remember first i said Note that the Angle is in Radians..

We must first convert from Radians to Degree..

Using this formula

`Degree rArr radians xx 180/pi`

Hence `rArr` `C^o = (5pi)/8 xx 180/pi`

`C^o = (5cancelpi)/8 xx 180/cancelpi`

`C^o = 5/8 xx 180/1`

`C^o = (5 xx 180)/8`

`C^o = 900/8`

`C^o = 900/8`

`C^o = 112.5`

`C^o ~~ 113`

Now to find c we shall using the Cosine Rule Formula

`c^2 = a^2 + b^2 - 2ab Cos(C)`

Imputing your values..

`c^2 = 7^2 + 5^2 - 2 xx 7 xx 5 Cos(113)`

`c^2 = 49 + 25 - 70 (-0.39073)`

`c^2 = 74 + 27.3511`

`c^2 = 101.3511`

`c^2 ~~ 101`

`c = sqrt101`

`c = 10.04987`

`c ~~ 10`

`:. c = 10 -> Answer`