Q: In a right triangle the of an angle is the length of the opposite side divided by the length of the adjacent side.?

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Consider the meaning of the sine and cosine functions. They are ratios of the side lengths in a right triangle. Sine is the length of the side opposite the angle, divided by that of the hypotenuse, and cosine is the length of the adjacent side, again, divided by the length of the hypotenuse. Consider then: sin = o/h cos = a/h This means that according to our problem, if x is the angle we're measuring in the triangle: -(o / h) - (a / h) = 0 ∴ -o - a = 0 ∴ a = -o Which tells us that the opposite and adjacent sides on our triangle are of equal length. This means that our triangle is not only a right triangle, but an isosceles triangle as well. That means that our angle (x) must be π/4, or 45°

There is no such thing as the tangent of a triangle. Circles, angles, and conversations have tangents. In a right angled triangle, the tangent of one of the acute angles is the ratio of the length of the side opposite the angle to the length of the side adjacent to it.

By using the trigonometric ratios of Sine and Cosine. The diagonal forms the hypotenuse of a right angled triangle with the length and width of the rectangle forming the other two sides of the triangle - the adjacent and opposite sides to the angle. Then: sine = opposite/hypotenuse → opposite = hypotenuse x sine(angle) cosine = adjacent/hypotenuse → adjacent = hypotenuse x cosine(angle)

There is the Pythagorean relationship between the side lengths. Given a right triangle with sides a, b, & c : Sides a & b are adjacent to the right angle, and side c is opposite the right angle, and this side is called the hypotenuse. Side c is always the longest side, and can be found by c2 = a2 + b2 The 2 angles (which are not the right angle) will add up to 90° Given one of those angles (call it A), then sin(A) = (opposite)/(hypotenuse) {which is the length of the side opposite of angle A, divided by the length of the hypotenuse} cos(A) = (adjacent)/(hypotenuse), and tan(A) = (opposite)/(adjacent).

Using the mathematical principles of trigonometry, you will need to know the lengths of any two of the sides of the right-angled triangle in order to calculate the other angles. The ratios of the lengths can be looked up in tables (or a scientific calculator may be used) to find the angle. The three sides of a right angled triangle have names as follows:- Hypotenuse - the longest side of the triangle, opposite the right angle Adjacent - the side next to the angle you wish to know Opposite - the side opposite the angle you wish to know The ratios are named as follows:- Sine - ratio of length of Opposite divided by length of Hypotenuse Cosine - ratio of length of Adjacent dived by length of Hypotenuse Tangent - ratio of length of Opposite divided by length of Adjacent These can be remembered by the mnemonic SOH CAH TOA Depending on which sides have the known lengths, calculate the ratio and look up the value for the angle in the Sine, Cosine or Tangent table as applicable. Once the value for one angle is known, the value for the other angle is 90 minus the value of the known angle.

Related questions

The secant of an angle in a right triangle is the hypotenuse divided by the adjacent side. The tangent angle of a right triangle is the length of the opposite side divided by the length of the adjacent side.

It is a tangent.

Remember SOHCAHTOA which means, the Sin of an angle is equal to the Opposite side divided by the Hypotenuse, the Cos of an angle is equal to the Adjacent side divided by the hypotenuse, and the Tangent of an angle is equal to the Opposite side divided by the Adjacent side. So as long as you have two sides of a right triangle, then you can find the angles and the length of the third side.

In a right triangle,the sine (sin) of one of the acute angles is the length of the opposite side divided by the length of the hypotenuse.the cosine (cos) is the length of the adjacent side divided by the length of the hypotenuse.the tangent (tan) is the length of the opposite side divided by the length of the adjacent side.The three others, cotangent, secant and cosecant, are merely reciprocals of the first three.The inverse functions, arcsine, arccosine, and arctangent respectively, each takes as an input the ratio of two sides and outputs an angle.

In a right triangle,the sine (sin) of one of the acute angles is the length of the opposite side divided by the length of the hypotenuse.the cosine (cos) is the length of the adjacent side divided by the length of the hypotenuse.the tangent (tan) is the length of the opposite side divided by the length of the adjacent side.The three others, cotangent, secant and cosecant, are merely reciprocals of the first three.The inverse functions, arcsine, arccosine, and arctangent respectively, each takes as an input the ratio of two sides and outputs an angle.

Suppose ABC is a triangle. There is nothing in the question that requires the triangle to be right angled. Suppose AB is the side opposite to angle C and BC is a side adjacent to angle C. Then AB/BC = sin(C)/sin(A)

the tangent of an angle is equal to the length of the opposite side from the angle divided by the length of the side adjacent to the angle.

In a right triangle, the sine of one of the angles other than the right angle is the length of the side opposite the angle divided by the length of the hypotenuse (the side opposite the right angle), the cosine is the length of the side adjacent to the angle divided by the length of the hypotenuse, and the tangent is the length of the opposite side divided by the length of the adjacent side.

Consider the meaning of the sine and cosine functions. They are ratios of the side lengths in a right triangle. Sine is the length of the side opposite the angle, divided by that of the hypotenuse, and cosine is the length of the adjacent side, again, divided by the length of the hypotenuse. Consider then: sin = o/h cos = a/h This means that according to our problem, if x is the angle we're measuring in the triangle: -(o / h) - (a / h) = 0 ∴ -o - a = 0 ∴ a = -o Which tells us that the opposite and adjacent sides on our triangle are of equal length. This means that our triangle is not only a right triangle, but an isosceles triangle as well. That means that our angle (x) must be π/4, or 45°

There is no such thing as the tangent of a triangle. Circles, angles, and conversations have tangents. In a right angled triangle, the tangent of one of the acute angles is the ratio of the length of the side opposite the angle to the length of the side adjacent to it.

By using the trigonometric ratios of Sine and Cosine. The diagonal forms the hypotenuse of a right angled triangle with the length and width of the rectangle forming the other two sides of the triangle - the adjacent and opposite sides to the angle. Then: sine = opposite/hypotenuse → opposite = hypotenuse x sine(angle) cosine = adjacent/hypotenuse → adjacent = hypotenuse x cosine(angle)

There is the Pythagorean relationship between the side lengths. Given a right triangle with sides a, b, & c : Sides a & b are adjacent to the right angle, and side c is opposite the right angle, and this side is called the hypotenuse. Side c is always the longest side, and can be found by c2 = a2 + b2 The 2 angles (which are not the right angle) will add up to 90° Given one of those angles (call it A), then sin(A) = (opposite)/(hypotenuse) {which is the length of the side opposite of angle A, divided by the length of the hypotenuse} cos(A) = (adjacent)/(hypotenuse), and tan(A) = (opposite)/(adjacent).