Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the
angle measures of the two acute angles.
fill in the missing information.
text should be lower case.
calculate the value for x.
answer (round to nearest degree): x =

Explanation:

Step1: Recall the tangent ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For angle \(X\), the side opposite is \(18\) and the side adjacent is \(\sqrt{35^{2}-18^{2}}=\sqrt{(35 + 18)(35 - 18)}=\sqrt{53\times17}=\sqrt{901}\approx30\) (using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 35\), \(a = 18\), and \(b\) is the adjacent side). But using the SOHCAHTOA mnemonic directly (since we know the two legs relative to angle \(X\)), \(\tan X=\frac{18}{30}\) (simplifying \(\frac{18}{30}=\frac{3}{5}\)).

Step2: Calculate the angle \(X\)

We know that \(X=\tan^{- 1}(\frac{18}{30})\). Using a calculator, \(X=\tan^{-1}(0.6)\).

$$X=\tan^{-1}(0.6)\approx31^{\circ}$$

Answer:

\(\tan X=\frac{18}{30}\), \(X = 31^{\circ}\)