Question

What is the tangent ratio of KJL? (Question and answers provided in picture.)

Answer 1

Answer:

Option (1)

Step-by-step explanation:

The given triangle JKL is an equilateral triangle.

Therefore, all three sides of this triangle will be equal in measure.

Side JK = JL = KL = 48 units

Perpendicular LM drawn to the base JK bisects the base in two equal parts JM and MK.

By applying tangent rule in ΔJML,

tan(∠KJL) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

                = $\frac{\text{LM}}{\text{JM}}$

                = $\frac{\text{LM}}{24}$

Since, Sin(K) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Sin(60)° = $\frac{\text{LM}}{48}$

$\frac{\sqrt{3}}{2}=\frac{\text{LM}}{48}$

LM = 24√3

Now, tan(∠KJL) = $\frac{\text{LM}}{24}$

                          = $\frac{24\sqrt{3} }{24}$

Therefore, Option (1) will be the answer.