Question

right triangle trigonometry - sohcahtoa
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: Recall inverse - trig function

To find an angle given a trigonometric ratio, use inverse trig functions. If $\sin\theta = x$, then $\theta=\sin^{- 1}(x)$; if $\cos\theta = x$, then $\theta=\cos^{-1}(x)$; if $\tan\theta = x$, then $\theta=\tan^{-1}(x)$.

Step2: Calculate $C$

$C = \sin^{-1}(0.7771)\approx51^{\circ}$ (using a calculator in degree - mode).

Step3: Calculate $Z$ (from $\cos Z$)

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

Step4: Calculate $X$

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

Step5: Calculate $A$ (from $\cos A$)

$A=\cos^{-1}(0.5000) = 60^{\circ}$.

Step6: Calculate $Z$ (from $\sin Z$)

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

Step7: Calculate $W$

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

Step8: Calculate $V$

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

Step9: Calculate $B$

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

Step10: Calculate $A$ (from $\tan A$)

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

Answer:

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