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).
sin c = 0.7771 ; c =
cos z = 0.3090 ; z =
sin x = 0.4540 ; x =
cos a = 0.5000 ; a =
sin z = 0.8572 ; z =
cos w = 0.1736 ; w =
tan v = 0.2126 ; v =
tan b = 0.9325 ; b =
tan a = 3.2709 ; a =

Explanation:

Step1: Calculate \(C\)

Given \(\sin C=0.7771\). Using the inverse - sine function \(C = \sin^{-1}(0.7771)\).
\(C=\sin^{-1}(0.7771)\approx51^{\circ}\)

Step2: Calculate \(Z\) (for \(\cos Z = 0.3090\))

Using the inverse - cosine function \(Z=\cos^{-1}(0.3090)\).
\(Z=\cos^{-1}(0.3090)\approx73^{\circ}\)

Step3: Calculate \(X\)

Given \(\sin X = 0.4540\). Using the inverse - sine function \(X=\sin^{-1}(0.4540)\).
\(X=\sin^{-1}(0.4540)\approx27^{\circ}\)

Step4: Calculate \(A\) (for \(\cos A=0.5000\))

Using the inverse - cosine function \(A = \cos^{-1}(0.5000)\).
\(A=\cos^{-1}(0.5000)=60^{\circ}\)

Step5: Calculate \(Z\) (for \(\sin Z = 0.8572\))

Using the inverse - sine function \(Z=\sin^{-1}(0.8572)\).
\(Z=\sin^{-1}(0.8572)\approx59^{\circ}\)

Step6: Calculate \(W\)

Given \(\cos W = 0.1736\). Using the inverse - cosine function \(W=\cos^{-1}(0.1736)\).
\(W=\cos^{-1}(0.1736)\approx80^{\circ}\)

Step7: Calculate \(V\)

Given \(\tan V=0.2126\). Using the inverse - tangent function \(V=\tan^{-1}(0.2126)\).
\(V=\tan^{-1}(0.2126)\approx12^{\circ}\)

Step8: Calculate \(B\)

Given \(\tan B = 0.9325\). Using the inverse - tangent function \(B=\tan^{-1}(0.9325)\).
\(B=\tan^{-1}(0.9325)\approx43^{\circ}\)

Step9: Calculate \(A\) (for \(\tan A = 3.2709\))

Using the inverse - tangent function \(A=\tan^{-1}(3.2709)\).
\(A=\tan^{-1}(3.2709)\approx73^{\circ}\)

Answer:

$C = 51^{\circ}$, $Z = 73^{\circ}$, $X = 27^{\circ}$, $A = 60^{\circ}$, $Z = 59^{\circ}$, $W = 80^{\circ}$, $V = 12^{\circ}$, $B = 43^{\circ}$, $A = 73^{\circ}$