Question

Find a in degrees.
a
6
√11
5
? ]°
Round to the nearest hundredth.

Answer 1

Answer:

33.55

Step-by-step explanation:

• $sin \alpha = \sqrt{11} \div 6$
• $\alpha = {sin}^{ - 1} 0.5527$
• $\alpha = 33.55$

Answer 2

Answer:

α = 33.56°  (nearest hundredth)

Step-by-step explanation:

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

• $\theta$ is the angle
• O is the side opposite the angle
• A is the side adjacent the angle
• H is the hypotenuse (the side opposite the right angle)

Given:

• $\theta=\alpha$
• O = $\sf \sqrt{11}$
• A = 5
• H = 6

As all sides of the right triangle have been given, any of the trigonometric ratios can be used to find α.

Sine Ratio

$\begin{aligned}\sf \sin(\alpha) & = \sf \dfrac{\sqrt{11}}{6}\\\implies \alpha & = \sf \sin^{-1}\left(\dfrac{\sqrt{11}}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}$

Cosine Ratio

$\begin{aligned}\sf \cos(\alpha) & =\sf \dfrac{5}{6}\\\implies \alpha & = \sf \cos^{-1}\left(\dfrac{5}{6}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}$

Tangent Ratio

$\begin{aligned}\sf \tan(\alpha) & =\sf \dfrac{\sqrt{11}}{5}\\\implies \alpha & = \sf \tan^{-1}\left(\dfrac{\sqrt{11}}{5}\right) \\& = \sf 33.55730976...^{\circ}\end{aligned}$

Therefore, α = 33.56°  (nearest hundredth)

Learn more about trigonometric ratios here:

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