Question

A right triangle has side lengths that are consecutive integers and a perimeter of 12 feet. What are the angles of the triangles?

Answer 1

36.87, 53.13, 90 degrees

side lengths

since its side lengths (a,b,c) are consecutive integers, we can say that

a = smallest side

b = a + 1

c = a + 2

perimeter = a + b + c = a + (a + 1) + (a + 2) = 3a + 3

perimeter = 12

3a + 3 = 12

3a = 9

a = 3

so the three side lengths are 3, 4, and 5

angles

since this is a right triangle, one angle is 90 degrees

(look at picture below to see where angles A and B are)

for angle A, we can use sinA = opposite/hypotenuse

sinA = 3/5

A =
`sin^(-1) ((3)/(5) )`

A = 36.87 degrees

since all three angles in a triangle add up to 180, we can find angle B through 180 = A + B + 90

B = 180 - 90 - 36.87

B = 53.13 degrees