What is the length of the missing side?

9514 1404 393

  10

Step-by-step explanation:

The Pythagorean theorem tells you the relationships of sides in a right triangle is ...

  a² + b² = c² . . . . . . where 'a' and 'b' are the legs, and 'c' is the hypotenuse

  6² +8² = c²

  36 +64 = c² = 100

  c = √100 = 10

The length of the hypotenuse is 10.

Additional comment

The ratio of the leg lengths is 8/6 = 4/3. The only right triangle with legs in the ratio 4/3 has the relationship ...

  hypotenuse : long leg : short leg = 5 : 4 : 3

If you multiply these numbers by 2, you see they correspond to the side lengths in this triangle. Your familiarity with a 3-4-5 right triangle can let you write down the answer immediately.

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

5.5

step-by-step explanation: