Numerical Trigonometry

Trigonometry Trigonometric ratios used with right triangles

To the nearest meter, how far is it across the river?

To the nearest centimeter, how high is the tree?

A cantilever home extends 4 meters from the side of a hill. The floor makes an angle measuring 48  with the hill. How far is the other edge of the floor vertically for the side of the hill?

A ramp 300 cm long is dropped from the rear of a furniture truck to the ground. If the ramp makes an angle measuring 12  with the ground, to the nearest centimeter, how high is the bed of the truck from the ground?

To the nearest degree what is the measure of the angle formed with the ground by a ladder 320 cm long if the ladder is leaning against a wall at a height of 280 cm?

If an airplane flies 3  off course for 400 kilometers, to the nearest kilometer, how far away from the correct path will the airplane then be?

Definitions  CAB is an angle of elevation.  SRQ is an angle of depression.

A surveyor finds that the angle of elevation from a point on level ground to the top of a building 110 meters high measures 18 . How far is the point on the ground from the base of the building?

An oil well is drilled on a slant line having an angle of depression with the level ground measuring 58 . How far below the surface is the drill bit when 1800 meters of the drill rod is in the ground?

A diving submarine travels through the water at a steady rate of 280 meters per minute on a diving path that forms an angle of depression measuring 5  with the surface of the water. How far beneath the surface is the submarine after 6 minutes?

The Capps Building is 98 meters in height, and is located 120 meters from the Sullivan Building. If the angle of elevation from the top of the Capps Building to the top of the Sullivan Building measures 31 , how tall is the Sullivan building?

A ladder 20 feet in length touches a wall at a point 16 feet above the ground. Find the angle the ladder makes with the ground.

A monument is 550 feet high. What is the length of the shadow cast by the monument when the sun is 64  above the horizon?

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