Question

If triangle ABC is an equilateral triangle and BD = 36 inches, find the value of x

Answer 1

Answer:

The value of x is $24\sqrt{3}\ in$

Step-by-step explanation:

we know that

An equilateral triangle has three equal sides and three equal internal angles (each internal angle measure 60 degrees)

In this problem

see the attached figure to better understand the problem

In the right triangle ABD

$sin(60\°)=BD/AB$

Solve for AB

$AB=BD/sin(60\°)$

we have

$BD=36\ in$

$sin(60\°)=\frac{\sqrt{3}}{2}$

substitute

$AB=36/(\frac{\sqrt{3}}{2})=24\sqrt{3}\ in$

Answer 2

Using the sine ratio, the value of x in the equilateral triangle is: 24√3 inches.

What is the Sine Ratio?

The sine ratio used to solve a right triangle is given as, sin ∅ = opposite side/hypotenuse.

Given the following:

• ∅ = 60 degrees; sin 60 = √3/2
• Opposite length = 36 inches
• Hypotenuse length = x

Apply the sine ratio:

sin 60 = 36/x

√3/2 = 36/x

x = 36/√3/2

x = (36 × 2)/√3

x = 72/√3

Rationalize

x = (72)(√3) / (√3)(√3)

x = 72√3 / 3

x = 24√3

Learn more about the sine ratio on:

https://brainly.com/question/2920412

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