A board with a length of 15 feet is leaning against a vertical wall at a point that is 12 feet above the ground. The angle that the board forms with the ground is 53.13°. Use a trigonometric function to determine the distance from the bottom of the board to the edge of the wall. In at least four sentences, explain why you chose your specific function and how it applies to the reference angle A. Be sure to include the key vocabulary words "sine", "ratio", "opposite side", "hypotenuse" and "angle measure" in your response. Describe each computational step in complete sentences.

Marina baked cookies. she gave 3/4 of the cookies to the scout bake sale. she shared the remaining 6 cookies with her friends. how many cookies did marina bake?

What is the value of the discriminant of the quadratic equation -2x = -8x + 8 and what does its value mean about thenumber of real number solutions the equation has?

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality