The ratio of the angle measures of the triangle are 3:1:5.if the longest side of the triangle is 15ft .the shortest side of the triangle is?

≈ 5.2 ft

Step-by-step explanation:

sum the parts of the ratio, 3 + 1 + 5 = 9 parts

Divide the angle sum of a triangle by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio, then

3 parts = 3 × 20° = 60°

5 parts = 5 × 20° = 100°

The angles of the triangle are 100°, 60° and 20°

The longest side is opposite the largest angle in the triangle

The shortest side is opposite the smallest angle in the triangle.

Thus

the longest side is opposite 100°

the shortest side is opposite 20°

let x represent the shortest side and using the Sine rule

= ( cross- multiply )

x × sin100° = 15sin20° ( divide both sides by sin100° )

x = ≈ 5.2 ( to the nearest tenth )

Thus the shortest side is ≈ 5.2 ft

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4