Question

IMPORTANT, PLEASE HELP QUICKLY! 40 POINTSS

Answer the following questions given that Angles A and B are the acute
angles found in a right triangle.

1. If tan (A) = 3/4, then tan (B) equals?

2. If tan (B) = 2/7, then tan (A) equals?

3. Based on the information in #2, which angle would be bigger, A or B?
Use a diagram to help justify your answers.

Answer 1

`\sf 1. \quad \tan(B)=(4)/(3)`

`\sf 2. \quad \tan(A)=(7)/(2)`

`\sf 3. \quad \angle A`

Explanation:

Acute angle: an angle less than 90°

Tan trigonometric ratio

`\sf \tan(\theta)=(O)/(A)`

where:

• 
  `\theta` is the angle
• O is the side opposite the angle
• A is the side adjacent the angle

Question 1

Refer to the first attached diagram.

If tan(A) = 3/4 then the side opposite ∠A is 3 units, and the side adjacent ∠A is 4 units.

Therefore:

`\implies \sf \tan(B)=(4)/(3)`

Question 2

Refer to the second attached diagram.

If tan(B) = 2/7 then the side opposite ∠B is ,and the side adjacent ∠B is 7.

Therefore:

`\implies \sf \tan(A)=(7)/(2)`

Question 3

Angle A would be bigger (see second attachment).