From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40º. If the tower is 45 feet in height, how far is the partner from the base of the tower, to the nearest tenth of a foot?
The "angle of depression" is from a horizontal line of sight downward. • It is assumed that the tower is vertical, making it perpendicular with the ground. • This solution will use alternate interior angles from the parallel horizontal lines, so place 40º inside the triangle by the partner (bottom right). • This solution deals with "opposite" and "adjacent" making it a tangent problem. tan 40 degrees = 45 / x = 0.839 x = 53.6 feet
Solve for the variable: 1 + x = 10
1 + x = 10 x = 10 - 1 x = 9
Solve 30 - 12÷3×2 =
According to order of operations (PEMDAS), 12÷3×2 (division and multiplication) is done first from left to right 12÷3×2 = 4 × 2 = 8 Hence 30 - 12÷3×2 = 30 - 8 = 22