Determine whether the given lengths can be side lengths of right triangle. 1. 15, 36, 39 2. 3, 7, 10 3. 8, 15, 17 4. root3, root4, root5 5. 6, 7, 8, 6. 12, 16, 20

Answers

1. YES

2. NO

3. YES

4. NO

5. NO

6. YES

Explanation

A right triangle has a property that it side length must meet. That is the pythagorean theorem.

It states that; For a right triangle ABC, c²=a²+b². Where a, b and c are the opposite side lengths to angle A,B and C respectively.

Q1

15, 36, 39

The longer side is our c.

39² = 36² + 15²

1521 = 1296 + 225

1521 = 1521

This is true. So the side lengths are for a right triangle.

Q2

3, 7, 10

The longer side is our c.

10² = 2² + 7²

100 = 4 + 49

100 = 53

This is not true. So the side lengths are NOT for a right triangle.

Q3

The longer side is our c.

8, 15, 17

17² = 8² + 15²

289 =64 + 225

289 = 289

This is true. So the side lengths are for a right triangle.

Q4

The long side is our c.

Root3, Root4, Root5

(√5)² = (√4)² + (√3)²

5 = 4 + 3

5 = 7

This is not true. So the side lengths are NOT for a right triangle.

Q5

The longer side is our c.

6, 7, 8,

8² = 6² + 7²

64 = 36 + 49

64 = 85

This is not true. So the side lengths NOT are for a right triangle.

Q6.

The longer side is always the c

12, 16, 20

20² = 12² + 16²

400 = 144 + 256

400 = 400

This is true. So the side lengths are for a right triangle.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

answer by yourhope:

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