One of the skateboard ramps at the local ramp park is 27 feet long. If the ramp is built in the form of a right triangle and has a 35° incline, how high is the ramp off the ground at the upper edge. Use trigonometric ratios to solve this problem. Round to the nearest hundredth.
Draw a diagram: Ramp = hypotenuse of right triangle = 27 feet Vertical side (sin) = side opposite 35° angle = a Horizontal side (cos) = side adjacent to 35° = b Ratio: sin of an angle = side opposite/hypotenuse = a/27 Set up the equation: sin35 = a ------ 27 Solve the equation: Multiply 27 on both sides: 27 sin35 = a 27(0.573576) = 15.48656378 Rounded: 15.49 feet
The Young Politicians Club at a local high school wants to replace the worn rope on the flagpole in front of City Hall. Some of the students in the club want to use their geometry skills to compute how much rope they will need. The first step in doing so is to determine how high the flagpole is. They decide to use similar triangles to compute this height. One of the students in the group, who is 6 feet tall, cast a shadow that is 4 feet. The flagpole casts a shadow that is 14 feet. Using similar triangles, compute the height of the flagpole?
Define the variable: Let x = pole height Draw similar right triangles: Smaller triangle: Vertical side = 6 Horizontal side = 4 Larger triangle: Vertical side = x (The height of the flagpole.) Horitizontal side = 14 Set up the proportional equation: 6 = x ---- ----- 4 14 Solve using ‘cross multiplication’ 4x = 84 Divide by 4 each side: x = 21 feet The flagpole is 21 feet tall.
Newborn baby elephant seals are born, on average, weighing 70 pounds. Their mother’s milk is so rich, the newborn will gain as much as 8 pounds per day. Newborns nurse for approximately 26 days. Given this information, a) How long will it take for the newborn pup to double its weight, and b) How much will the pup weigh by the time its mother is done nursing her baby.
a) Define the variable: d = days Weight doubled: 2 x 70 = 140 pounds Algebraic equation: 70 + 8d = 140 Subtract 70 on both sides: 8d = 70 Divide by 8 on both sides: d = 8.75 ‘Days’ are defined by integers. Round up to d = 9 days b) Define the variable: w = weight Algebraic equation: 70 + 26(8) = w Solution: 70 + 208 = 278 pounds