SohCahToa/Law of Sines Review

Front

What does SohCahToa stand for?

Back

SohCahToa is a mnemonic for remembering the definitions of sine, cosine, and tangent in a right triangle: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.

Front

How do you calculate the sine of an angle in a right triangle?

Back

Sine of an angle = Length of the opposite side / Length of the hypotenuse.

Front

How do you calculate the cosine of an angle in a right triangle?

Back

Cosine of an angle = Length of the adjacent side / Length of the hypotenuse.

Front

How do you calculate the tangent of an angle in a right triangle?

Back

Tangent of an angle = Length of the opposite side / Length of the adjacent side.

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides: a/sin(A) = b/sin(B) = c/sin(C).

Front

How can you find an unknown angle using the Law of Sines?

Back

To find an unknown angle, rearrange the Law of Sines: sin(A) = a * sin(B) / b, then use the inverse sine function.

Front

What is the relationship between the angles and sides in a triangle?

Back

In any triangle, the larger the angle, the longer the opposite side; conversely, the smaller the angle, the shorter the opposite side.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7^2 + 24^2 = 25^2 (49 + 576 = 625).

Front

What is the formula for finding the area of a triangle using the sine of an angle?

Back

Area = 1/2 * a * b * sin(C), where a and b are two sides and C is the included angle.

Front

How do you find the length of a side using the Law of Sines?

Back

Rearrange the Law of Sines: a = b * sin(A) / sin(B) to find the length of side a.