Question

right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
calculate the value for each angle measure (round to the nearest degree).
sinc = 0.7771 ; c=
cosz = 0.3090 ; z=
sinx = 0.4540 ; x=
cosa = 0.5000 ; a=
sinz = 0.8572 ; z=
cosw = 0.1736 ; w=
tanv = 0.2126 ; v=
tanb = 0.9325 ; b=
tana = 3.2709 ; a=

Explanation:

Step1: Find angle C

$C = \sin^{- 1}(0.7771)\approx51^{\circ}$

Step2: Find angle Z

$Z=\cos^{-1}(0.3090)\approx72^{\circ}$

Step3: Find angle X

$X=\sin^{-1}(0.4540)\approx27^{\circ}$

Step4: Find angle A

$A=\cos^{-1}(0.5000)\approx60^{\circ}$

Step5: Find angle Z (second case)

$Z=\sin^{-1}(0.8572)\approx59^{\circ}$

Step6: Find angle W

$W=\cos^{-1}(0.1736)\approx80^{\circ}$

Step7: Find angle V

$V=\tan^{-1}(0.2126)\approx12^{\circ}$

Step8: Find angle B

$B=\tan^{-1}(0.9325)\approx43^{\circ}$

Step9: Find angle A (second case)

$A=\tan^{-1}(3.2709)\approx73^{\circ}$

Answer:

$C\approx51^{\circ}$, $Z\approx72^{\circ}$, $X\approx27^{\circ}$, $A\approx60^{\circ}$, $Z\approx59^{\circ}$, $W\approx80^{\circ}$, $V\approx12^{\circ}$, $B\approx43^{\circ}$, $A\approx73^{\circ}$