Answer:
Image 1
[tex]\tan A = \frac{45}{24}= \frac{15}{8}[/tex]
[tex]\tan B = \frac{24}{45} = \frac{8}{15}[/tex]
Image 2
[tex]\tan D = \frac{15}{36} = \frac{5}{12}[/tex]
[tex]\tan E = \frac{36}{15} = \frac{12}{5}[/tex]
Image 3
[tex]\tan P = \frac{32}{24} = \frac{4}{3}[/tex]
[tex]\tan Q = \frac{24}{32} = \frac{3}{4}[/tex]
Step-by-step 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
[tex]\tan A = \frac{45}{24}= \frac{15}{8}[/tex]
[tex]\tan B = \frac{24}{45} = \frac{8}{15}[/tex]
Image 2
[tex]\tan D = \frac{15}{36} = \frac{5}{12}[/tex]
[tex]\tan E = \frac{36}{15} = \frac{12}{5}[/tex]
Image 3
[tex]\tan P = \frac{32}{24} = \frac{4}{3}[/tex]
[tex]\tan Q = \frac{24}{32} = \frac{3}{4}[/tex]
