So, the Pythagorean Theorem is a special case of the Law of Cosines. Find the remaining side and angles. To find the remaining angles, it is easiest to now use the Law of Sines. Note that angle A is opposite to the longest side and the triangle is not a right triangle. Find the measures of the angles.
It is best to find the angle opposite the longest side first. In this case, that is side b. Since cos B is negative, we know that B is an obtuse angle. Since B is an obtuse angle and a triangle has at most one obtuse angle, we know that angle A and angle C are both acute. To find the other two angles, it is simplest to use the Law of Sines.
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If you were happy that the unit worked correctly, please click the button on the right. If you found any problems or would like to add any comments, please fill out the form below and click on the send button. If you need to find the length of a side, you need to use the version of the Sine Rule where the lengths are on the top:. Work out the length of x in the diagram below:. Start by writing out the Sine Rule formula for finding sides:. Fill in the values you know, and the unknown length:.
Solve the resulting equation to find the unknown side, giving your answer to 3 significant figures:. If you need to find the size of an angle, you need to use the version of the Sine Rule where the angles are on the top:. Start by writing out the Sine Rule formula for finding angles:. Fill in the values you know, and the unknown angle:. Solve the resulting equation to find the sine of the unknown angle:. Work out the answer to each question then click on the button marked to see if you are correct.
If you need to find the length of a side, you need to know the other two sides and the opposite angle. Evaluate the right-hand-side and then square-root to find the length: x 2. If you need to find the size of an angle, you need to use the version of the Cosine Rule where the cos A is on the left: cos A.
Start by writing out the Cosine Rule formula for finding angles: cos A. Sometimes more than one technique from the formula table at the top of this page can be used to solve a trig problem, but you will want to choose the most efficient and easiest method to save time.
The flowchart below shows how to decide which method to use:. The triangle is not right-angled. The triangle is right-angled. The triangle to the right of the dotted line is right-angled, so use the appropriate trig ratio sin, cos or tan. After finding x you have enough information to use trigonometry in the right-angled triangle above the dotted line. Correct Answers You answered 0 questions correctly out of the questions in this section.
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