Identify the angle of elevation from point C to point A in the given figure:
Identify the angle of depression from point B to point C in the given figure:
Find x, the angle of elevation to point A from point C. Round your answer to two decimal places.
Sally measures the angle of elevation to the top of a tree from a point 20 \text{ m} away to be 43 \degree.
Find the height of the tree, h, to the nearest whole number.
A helicopter is flying at an altitude of 198 \text{ m}. Its landing pad is at an angle of depression of 44 \degree.
Determine the distance, d, between the helicopter and the landing pad. Round your answer to the nearest whole number.
The final approach of an aeroplane when landing requires the pilot to adjust the angle of descent to about 3 \degree as shown in the diagram below. If the plane is 12 \text{ m} above the runway and has d \text{ m} until touchdown, find d to the nearest metre.
A soft drink can has a height of 11 \text{ cm} and a radius of 4 \text{ cm}. Find L, the length of the longest straw that can fit into the can.
Round your answer down to the nearest centimetre, to ensure the straw fits inside the can.
\triangle ABC consists of angles A, B and C which appear opposite sides a, b and c respectively. If the measures of a, c and A are given, which rule should be used to find the size of \angle C, the sine rule or the cosine rule?
A student created a scale model of Australia and drew a triangle between Alice Springs, Brisbane and Adelaide:
Find the angle \theta, between Brisbane and Adelaide from Alice Springs. Round your answer to one decimal place.
Hence or otherwise, find the area taken up by the triangle. Round your answer to two decimal places.
For the following diagram, calculate the length of y in metres. Round your answer to one decimal place.
Consider the following diagram:
Calculate the value of y. Round your answer to one decimal place.
Calculate the value of x. Round your answer to two decimal places.
Consider the following diagram:
Find the value of \theta. Round your answer to two decimal places.
Hence or otherwise, find the value of d. Round your answer to one decimal place.
For the following diagram, find the length of side y.
Round your answer to two decimal places.
Three points A, B and C are in a straight line. A vertical tower of height 35 \text{ m} stands at C. The angle of elevation of the top of the tower from A is 34 \degree and from B is 43 \degree.
Calculate the distance from A to B. Round your answer to two decimal places.
A jet takes off and leaves the runway at an angle of 34 \degree. It continues to fly in this direction for 7 \text{ min} at a speed of 630 \text{ km/h} before levelling out.
Find the distance in metres covered by the jet just before levelling out.
If the height of the jet just before levelling out is h \text{ m}, calculate h.
Round your answer to the nearest metre.
From the cockpit of an aeroplane flying at an altitude of 3000 \text{ m}, the angle of depression to the airport is 57 \degree. The aeroplane continues to fly in the same straight line, and after a few minutes the angle of depression to the airport becomes 67 \degree.
The horizontal distance between the cockpit at the first sighting and the point directly above the airport is x \text{ m}.
Find the value of x. Round your answer to one decimal place.
The horizontal distance between the cockpit at the second sighting and the point directly above the airport is y \text{ m}.
Find the value of y. Round your answer to one decimal place.
Find x, the angle of depression from point B to point C in the diagram below:
Round your answer to two decimal places.
A man stands at point A looking at the top of two poles. Pole 1 has a height 8 \text{ m} and an angle of elevation of 34 \degree from point A. Pole 2 has a height 25 \text{ m} and an angle of elevation of 57 \degree from point A.
Find x, the distance from A to B, to two decimal places.
Find y, the distance from A to C, to two decimal places.
Hence, find BC, the distance between the two poles in metres. Round your answer to one decimal place.
Mandy is standing 4 \text{ km} away from home on a bearing of \text{N } 32 \degree \text{E}.
Calculate the vertical distance, x, between Mandy and home. Round your answer to two decimal places.
Consider the following diagram:
Calculate the direct distance from P to Q. Round your answer to two decimal places.
Calculate the area enclosed by triangle POQ. Round your answer to two decimal places.
Calculate the true bearing of Q from P, correct to two decimal places.
Farmer Joe has a trapezoidal shaped paddock. He is trying to calculate the area and has some of the measurements of the paddock as shown on the diagram:
Determine the area of his paddock as illustrated on the first diagram. Round your answer to two decimal places.
For the neighbouring paddock, Farmer Joe’s son Jack decides he can determine the area with fewer measurements.
Determine the area of the neighbouring paddock as indicated in the second diagram. Round your answer to two decimal places.
Jim and Bob both cycle from their house. Jim travels 120 \text{ m} on a bearing of 120 \degree while Bob travels 200 \text{ m} on a bearing of 60 \degree.
Determine the distance, x \text{ m}, between Jim and Bob. Round your answer to one decimal place.
Determine the bearing of Jim from Bob. Round your answer to one decimal place.
Anthony is at the park with his dogs Juddy and Nelson. Juddy runs off on a bearing of 115 \degree and runs for 21 \text{ m} before stopping to sniff a tree. Nelson then leaves Anthony to lie in the shade 32 \text{ m} away on a bearing of 211 \degree. Juddy and Nelson are 40 \text{ m} apart.
Determine the bearing of Anthony from Juddy.
Determine the bearing of Nelson from Juddy.
Mary and Jane are on opposite sides of a valley. They both look down into the valley between them and see a large kangaroo. Mary is 7.5 \text{ m} above the valley and sees the kangaroo at an angle of depression of 49 \degree. Jane is 5.9 \text{ m} higher than Mary and the angle of elevation from the kangaroo to Jane is 40 \degree.
Assuming Mary and Jane are both standing at the edges of cliffs at each side of the valley, determine the width of the valley to one decimal place.
Calculate the straight line distance between Mary and Jane. Round your answer to two decimal places.
A fighter jet, flying at an altitude of 2000 \text{ m} is approaching an airport. The pilot measures the angle of depression to the airport to be 13 \degree. One minute later, the pilot measures the angle of depression again and finds it to be 16 \degree.
Find the distance covered by the jet in that one minute, to the nearest metre.