Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

25 points!!!!!!!!!!!!!!!!!!
The length of the hypotenuse of 30 - 60 - 90 a triangle is 6. Find the perimeter. Round answer to the nearest hundredth.

Sagot :

amysun2025

Answer:

14.2

Step-by-step explanation:

Hi there!

We are given a 30-60-90 triangle

The triangle is a right triangle, since one of the angles measures 90 degrees

We are also given that the length of the hypotenuse (the side OPPOSITE from the right angle) is 6

We want to find the perimeter of the triangle

There are special formulas to find the other sides of the triangle, if we know that:

a. the triangle is a right triangle

b. we know the length of the hypotenuse

These two formulas are:

  • If the length of the hypotenuse in a triangle is a, then the length of the side OPPOSITE from the 30 degree angle is [tex]\frac{a}{2}[/tex]
  • The length of the side OPPOSITE from the 60 degree angle is [tex]\frac{a\sqrt{3} }{2}[/tex]

In this problem, we are given that a=6, so that means that in order to find the length of the other sides:

The length of the side opposite from the 30° angle: [tex]\frac{a}{2} = \frac{6}{2} = 3[/tex]

The length of the side opposite from the 60° angle: [tex]\frac{a\sqrt{3} }{2} = \frac{6\sqrt{3} }{2} = 3\sqrt{3}[/tex], or about 5.2

Now, to find the perimeter, we add the lengths of these sides together.

6 + 3 + 5.2 = 14.2

Hope this helps!

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.