6.04 Applications of trigonometry
If d is the distance between the base of the wall and the base of the ladder, find the value of d to two decimal places.
Find the height of the tree, h, to two decimal places:
A ladder is leaning at an angle of 44 \degree against a 1.36 \text{ m} high wall.
Find the length of the ladder l, to two decimal places.
Georgia is riding her pushbike up a hill that has an incline of 5 \degree.
If she rides her bike 817\text{ m} up the hill, find d, the horizontal distance from where she started, to the nearest metre.
Mohamad is standing at the tip of a tree's shadow and knows that the angle from the ground to the top of the tree is 27 \degree.
If Mohamad is standing 19\text{ m} away from the base of the tree, find h, the height of the tree, to two decimal places.
The longer side of a rectangular garden measures 10\text{ m}. A diagonal path makes an angle of 26\degree with the longer side of the garden.
If the length of the shorter side of the garden is y\text{ m}, find y 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 the distance from A to B, to two decimal places.
Find 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.
A sand pile has an angle of 40 \degree and is 10.6 \text{ m} wide.
Find the height of the sand pile, h, to one decimal place.
A slide casts a shadow 5.66 \text{ m} along the ground. The distance between the tip of the shadow and the top of the slide is 7.84\text{ m}.
Find \theta to two decimal places.
A ladder measuring 1.65 \text{ m} in length is leaning against a wall. If the angle the ladder makes with the wall is y \degree, find y to two decimal places.
A ramp of length 311\text{ cm} needs to ascend at an angle between 10 \degree and 20 \degree for it to be safe to use.
If the height of the ramp is 152\text{ cm}, and the angle the ramp makes with the ground is x, find x to two decimal places.
If the height of the ramp is 25\text{ cm} , and the angle the ramp makes with the ground is y, find y to two decimal places.
If the height of the ramp is 100\text{ cm}, and the angle the ramp makes with the ground is z, find z to two decimal places.
Hence, at which height is the ramp safe?
A ladder measuring 2.36 \text{ m} in length is leaning against a wall.
If the angle the ladder makes with the ground is x, find the value of x to two decimal places.
In the diagram, a string of lights joins the top of the tree to a point on the ground 23.9 \text{ m} away. If the angle that the string of lights makes with the ground is \theta, find \theta to two decimal places.
During a particular time of the day, a tree casts a shadow of length 24\text{ m}. The height of the tree is estimated to be 7\text{ m}. Find the angle \theta, formed by the length of the shadow and the arm extending from the edge of the shadow to the top of the tree. Round your answer to two decimal places.
A ship dropped anchor off the coast of a resort. The anchor fell 83\text{ m} to the sea bed. During the next 4 hours, the ship drifted 105\text{ m}.
Find x, the angle between the anchor line and the surface of the water, to the nearest degree.
A 27.3\text{ m} long cable joins the top of a flagpole to a point on the ground.
If the flagpole is 7.4\text{ m} tall, find \theta, the angle the cable would make with the flagpole, 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.
Sketch a diagram of the situation.
Find the height of the tree, h, to the nearest whole number.
The person in the picture sights a pigeon above him. Find \theta to two decimal places.
A boy flying his kite releases the entire length of his string which measures 27\text{ m}, so that the kite is 18\text{ m} above him.
If the angle the string makes with the horizontal ground is \theta, find \theta to two decimal places.
The person in the picture sights a paraglider above him.
If the angle the person is looking at is a, find a to two decimal places.
The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10\,369 \text{ m} above the ground and is still 23\,444 \text{ m} from the runway.
If \theta \degree is the angle at which the plane should approach, find \theta to one decimal place.
A helicopter is 344\text{ m} away from its landing pad.
If the angle of depression to the landing pad is 32 \degree, find x, the height of the helicopter above the ground, to the nearest metre.
A helicopter is flying at an altitude of 198 \text{ m} from its landing pad, which is at an angle of depression of 44 \degree from the helicopter.
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 an angle of descent of about 4 \degree.
The plane is directly above a point 51 \text{ m} from the start of the runway.
Sketch a diagram of the situation.
Find d, the height of the plane above the ground to the nearest metre.
The angle of elevation from an observer to the top of a building is 65\degree. If the observer is 20 metres from the base of the building, find the height of the building to two decimal places.
From the top of a rocky ledge 261 \text{ m} high, the angle of depression to a boat is 8\degree. If the boat is d \text{ m} from the foot of the cliff find d correct to two decimal places.