Question

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

angles of the triangle?
А. 30°, 60° and 90°
B. 33.47°, 56.53° and 90°
C. 36.87°, 53.13° and 90°
D. 40.16°, 49.84° and 90°

Answer 1

option c

Explanation:

Let the sides of the right angled triangle = x , (x +1) , (x +2)

Perimeter = 12 feet

x + x +1 + x + 2 = 12

x +x + x + 1+2 = 12

Combine like terms

3x+ 3 = 12

Subtract 3 from both sides

3x = 12- 3

3x = 9

Divide both sides by 3

x = 9/3

x = 3

x + 1 = 3 + 1 = 4

x + 2 = 3 + 2 = 5

The sides of the triangle are 3 , 4 ,5

The biggest side will be the hypotenuse.

So, hypotenuse = 5 ft. other legs are 3 and 4

`\text {Sin \ $\theta$ = $(opposite \ side \ of \ \theta)/(hypotenuse)$ } \\\\\\ = (4)/(5)\\\\\\Sin \ \theta = 0.8\\\\\theta = Sin^(-1) \ 0.8\\\\\theta = 53.13 \ ^\circ`

another angle = 180 - [ 90 + 53.13]

= 180 - 143.13

= 36.87°