SOH CAH TOA Angle and Side Problems

Front

What does SOH CAH TOA stand for in trigonometry?

Back

SOH CAH TOA is a mnemonic for remembering the definitions of the sine, cosine, and tangent functions: SOH = Sine = Opposite/Hypotenuse, CAH = Cosine = Adjacent/Hypotenuse, TOA = Tangent = Opposite/Adjacent.

Front

How do you calculate the height of an object using the angle of elevation?

Back

To find the height (h) of an object using the angle of elevation (θ) and the distance (d) from the object, use the formula: h = d * tan(θ).

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The length of the hypotenuse (c) can be found using the Pythagorean theorem: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

If the angle of elevation to the top of a flagpole is 60 degrees and the height of the flagpole is 12 meters, how far is the point from the base?

Back

Using the formula h = d * tan(θ), we find d = h / tan(60°) = 12 / √3 ≈ 6.93 meters.

Front

What is the relationship between the angle of depression and the angle of elevation?

Back

The angle of depression from a point above the horizontal to an object below is equal to the angle of elevation from that object to the point.

Front

How do you find the length of a string attached to a kite at a height of 20 meters making a 60-degree angle with the ground?

Back

Using the formula: length = height / sin(θ), we find length = 20 / sin(60°) = 20 / (√3/2) = 20 * (2/√3) ≈ 23.09 meters.

Front

What is the height of a lighthouse if a ship is 100 meters away and the angle of depression is 30 degrees?

Back

Using the formula: height = distance * tan(30°), we find height = 100 * tan(30°) = 100 * (1/√3) ≈ 86.6 meters.

Front

How do you calculate the height of a building if the angle of elevation is 45 degrees and the distance from the building is 50 meters?

Back

Using the formula: height = distance * tan(θ), we find height = 50 * tan(45°) = 50 * 1 = 50 meters.

Front

What is the height of a bridge that is 100 meters long and makes a 10-degree angle with the horizontal?

Back

Using the formula: height = length * sin(θ), we find height = 100 * sin(10°) ≈ 17.36 meters.

Front

Define sine in terms of a right triangle.

Back

Sine (sin) of an angle is the ratio of the length of the opposite side to the length of the hypotenuse: sin(θ) = Opposite/Hypotenuse.