A boat is 300m away from the foot of a cliff. The angle of elevation from the boat to the top of the cliff is 16 degrees.
a) Determine the height of the cliff to the nearest meter.
b) If the boat sails 75 m closer to the cliff, determine , to the nearest degree, the new angle of elevation of the cliff top from the boat.
tan16=h/300 or h=300*tan16
tanTheta=h/(225) put in h, then determine tan theta, then
theta=arctan(h/225)
A school with 360 pupils travelled to the zoo for a day trip. There had to be at least 1 adult to every 7 pupils. What was the minimum number of adults needed for the trip?
To solve this problem, we can use trigonometry and the properties of right triangles.
a) To find the height of the cliff, we can use tangent function. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the height of the cliff is the opposite side, and the distance from the boat to the cliff is the adjacent side.
Let's denote the height of the cliff as h.
Using the tangent function: tan(16 degrees) = h / 300m
To find h, we can rearrange the equation:
h = tan(16 degrees) * 300m
Using a calculator, we can calculate:
h ≈ 88.91m
Therefore, the height of the cliff is approximately 88.91 meters.
b) If the boat sails 75 meters closer to the cliff, the new distance from the boat to the cliff will be 300m - 75m = 225m.
To find the new angle of elevation from the boat to the top of the cliff, we can again use the tangent function. Let's denote the new angle of elevation as θ.
Using the tangent function: tan(θ) = h / 225m
where h is the height of the cliff we found in part a.
To find θ, we can rearrange the equation:
θ = arctan(h / 225m)
Using a calculator, we can calculate:
θ ≈ 20.97 degrees
Therefore, the new angle of elevation of the cliff top from the boat, when the boat is 75 meters closer, is approximately 20.97 degrees.