# If sinx=55/65 then sinx +cosx = ?

Mar 29, 2018

$\frac{89.6}{65}$

#### Explanation:

Sine is the $\frac{o}{h}$ so we know the opposite is 55 and the hypotenuse is 65

So from this we can figure out the adjacent using Pythagoras

${c}^{2} = {a}^{2} + {b}^{2}$

${\left(65\right)}^{2} = {\left(55\right)}^{2} + {b}^{2}$

${\left(65\right)}^{2} = {\left(55\right)}^{2} + {b}^{2}$

$4225 = 3025 + {b}^{2}$

$1200 = {b}^{2}$

$b = 34.6$ (3sf)

$C o s \left(x\right) = \frac{a}{h} = \frac{34.6}{65}$

So $\sin \left(x\right) + \cos \left(x\right) = \frac{55 + 34.6}{65} = \frac{89.6}{65}$