Question

Find the tangent of each acute angle.

Answer 1

Answer:

Image 1

$\tan A = \frac{45}{24}= \frac{15}{8}$

$\tan B = \frac{24}{45} = \frac{8}{15}$

Image 2

$\tan D = \frac{15}{36} = \frac{5}{12}$

$\tan E = \frac{36}{15} = \frac{12}{5}$

Image 3

$\tan P = \frac{32}{24} = \frac{4}{3}$

$\tan Q = \frac{24}{32} = \frac{3}{4}$

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

$\tan A = \frac{45}{24}= \frac{15}{8}$

$\tan B = \frac{24}{45} = \frac{8}{15}$

Image 2

$\tan D = \frac{15}{36} = \frac{5}{12}$

$\tan E = \frac{36}{15} = \frac{12}{5}$

Image 3

$\tan P = \frac{32}{24} = \frac{4}{3}$

$\tan Q = \frac{24}{32} = \frac{3}{4}$