Question

Find the tangent of each acute angle.

Answer 1

Image 1

`\tan A = (45)/(24)= (15)/(8)`

`\tan B = (24)/(45) = (8)/(15)`

Image 2

`\tan D = (15)/(36) = (5)/(12)`

`\tan E = (36)/(15) = (12)/(5)`

Image 3

`\tan P = (32)/(24) = (4)/(3)`

`\tan Q = (24)/(32) = (3)/(4)`

Explanation:

Trigonometrically speaking, the tangent of an angle in a right triangle is the ratio of the length opposite to the angle to the length adjacent to the angle. Then, we solve for each case:

Image 1

`\tan A = (45)/(24)= (15)/(8)`

`\tan B = (24)/(45) = (8)/(15)`

Image 2

`\tan D = (15)/(36) = (5)/(12)`

`\tan E = (36)/(15) = (12)/(5)`

Image 3

`\tan P = (32)/(24) = (4)/(3)`

`\tan Q = (24)/(32) = (3)/(4)`