A skateboarding ramp is 12 in. high and rises at an angle of 21°. How long is the base of the ramp? Round to the nearest inch.

the base of the ramp is 31 inches long.

Step-by-step explanation:

c = a/sin(α)

=33.48514

b =√c2 - a2

=√33.4851373155042 - 122

=√977.25442103816

=31.26107

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.