Question

Analyze the diagram below and answer the question that follows.

Answer 1

Answer:

The right statement is sin(J) = cos(L) ⇒ answer D

Step-by-step explanation:

* Lets describe the figure

- LKJ is a right triangle, where K is a right angle

∵ m∠K = 90°

∵ LJ is opposite to angle K

∴ LJ is the hypotenuse

∵ LJ = 219

∵ KJ = 178

- By using Pythagoras Theorem

∵ (LJ)² = (LK)² + (KJ)²

∴ (219)² = (LK)² + (178)² ⇒ subtract (178)² from both sides

∴ (LK)² = (219)² - (178)²

∴ (LK)² = 16277

∴ LK = √16277 = 127.58

* Lets revise how to find the trigonometry function

# sin Ф = opposite/hypotenuse

# cos Ф = adjacent/hypotenuse

# tan Ф = opposite/adjacent

∵ LK is the opposite side to angle J

∵ LJ is the hypotenuse

∵ sin(J) = LK/LJ

∵ LK = 127.58 , LJ = 219

∴ sin(J) = 127.58/219 = 0.583

∵ LK is the adjacent side to angle L

∵ LJ is the hypotenuse

∵ cos(L) = LK/LJ

∵ LK = 127.58 , LJ = 219

∴ cos(L) = 127.58/219 = 0.583

∴ sin(J) = cos(L)

* The right statement is sin(J) = cos(L)