Question

Please help!

Inverse cosine is used to find a given angle measure when we know the ________ and the ________.
A. same side; other side
B. opposite side; hypotenuse
C. opposite side; adjacent side
D. adjacent side; hypotenuse

Answer 1

adjacent side and Hypotenuse

Explanation:

In a right angle triangle the sides are known as

• Perpendicular=Opposite side
• Base=Adjacent side
• Hypotenuse

So

• cosØ=Base/Hypotenuse
• cosØ=Adjacent/Hypotenuse

Hence option D is correct

Answer 2

D. adjacent side; hypotenuse

Explanation:

Trigonometric ratios

`\sf \sin(\theta)=(O)/(H)\quad\cos(\theta)=(A)/(H)\quad\tan(\theta)=(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)

Therefore, when the cosine trigonometric ratio is used to find a given angle, we take the inverse cosine of the ratio of the adjacent side to the hypotenuse:

`\implies \sf \theta = \cos^(-1)\left((A)/(H)\right)`