At a certain time of day, the angle of elevation of the sun is 30°. a tree has a shadow that is 25 feet long. find the height of the tree to the nearest foot.

Height of the tree = 14 feet

Step-by-step explanation:

The following illustration will form a right angle triangle. The tree will form the height which is the opposite side. The shadow cast by the tree will form the adjacent side while the angle of elevation is 30° to the hypotenuse.

Using SOHCAHTOA principle

TOA will be used to solve this

since the adjacent side is given which is the length of the shadow and we are looking for the opposite side which is the height of the tree.

shadow length(adjacent) = 25 feet

height of tree(opposite) = y

angle made with the ground = 30°

tan 30° = opposite/adjacent

tan 30° = y/25

cross multiply

25 × tan 30 = y

y =  0.5773502692  × 25

y =  14.43375673  feet

Height of the tree = 14 feet

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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step-by-step explanation: