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

The measures of the angles are 36.9 deg, 53.1 deg, 90 deg.

Step-by-step explanation:

The lengths of the sides are the famous Pythagorean triple: 3, 4, 5.

To find the angles, we use trigonometry.

Since it's a right angle, the longest side is the hypotenuse.

The hypotenuse has length 5.

The legs have lengths 3 and 4.

tan A = opp/adj

A = tan^(-1) opp/adj

A = tan^(-1) 4/3 = 53.1 deg

The acute angles of a right triangle are complementary.

B = 90 - A = 90 deg - 53.1 deg = 36.9 deg

The measures of the angles are 36.9 deg, 53.1 deg, 90 deg.

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

tap for more

y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: