Need help on geometry question

Question

The hypotenuse of 30°-60°-90° triangle is 3. Find the perimeter. the options are

•3√2 +3

•9/2 + 3/2 √3

•9/2 + 3/2 √2

•2√3 +2

Answer 1

Hi Samantha S.

Its the second option on your list

9/2 + 3/2 √3

According the information given, the Hypotenuse of a 30, 60,90 Right Triangle is 3 and you need to find the Perimeter. The Perimeter of a triangle is the sum of all its sides

For this question you can look up the relationship of the angles and sides of the special Right Triangles

This is probably in the text for your class and you can look it up online

For a 30, 60,90 Right Triangle the sides are related as follows:

The length of the Hypotenuse is twice the length of the side opposite the 30 degree angle or shortest side

The Square Root of the Hypotenuse times the length of the shortest side is the length of the side opposite the 60 degree angle

The side opposite the 30 degree angle is 3/2 = 1.5

The side opposite the 60 degree angle is 1.5√3

The Perimeter of the 30, 60, 90 Triangle is 3 + 1.5 + 1.5√3 = 3 + 3/2 + 3/2√3

Can you do the math and complete the answer

Answer 2

Hypotenuse has length 3

One leg has length 3*sin(30^o) = 3/2

The other leg has length 3*cos(30^o) = 3*(√3)/2 = (3/2)√3

Perimeter is just the sum of the above three side lengths:

Adding them up: 3 + 3/2 + (3/2)√3 = 6/2 + 3/2 + (3/2)√3 = 9/2 + (3/2)√3 (2nd answer on list of choices)