Question

Analyze the diagram below and complete the instructions that follow?

Answer 1

Answer:

The exact value of tan(M) is 5/12 ⇒ answer (C)

Step-by-step explanation:

* Lets revise the trigonometry functions

- In ΔABC

# m∠B = 90°

# Length of AB = a , length of BC = b and length of AC = c

# The trigonometry functions of angle C are

- sin(C) = a/c ⇒ opposite side to ∠C ÷ the hypotenuse

- cos(C) = b/c ⇒ adjacent side to ∠C ÷ the hypotenuse

- tan(c) = a/b ⇒ opposite side to ∠C ÷ adjacent side to ∠C

* Now lets solve the problem

- In ΔONM

∵ m∠N = 90°

∵ MN = 12

∵ ON = 5

∵ tan(M) = ON/NM ⇒ opposite side of ∠(M) ÷ adjacent side of ∠(M)

∴ tan(M) = 5/12

* The exact value of tan(M) is 5/12