The angle of elevation from a soccer ball on the ground to the top of the goal is 38 degrees. if the goal is 8 feet tall, what is the distance from the ball to the goal?

The distance is 10.24 feet ( to the nearest hundredth).

Step-by-step explanation:

Use trigonometry of a right angled triangle:

The angle = 38 degrees, opposite side = 8 ft, we require the adjacent side:  We have  opposite / adjacent side so we need the tangent.

tan 38 = 8 / a

a = 8 / tan 38

= 10.24 feet.

answer: group b.

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true