Finally, use the fact that the sum of the angles is 180 degrees to find the remaining third angle. Then use the sine rule to find another angle. You'll need to use the arccos or inverse cos function to work out the value of the angle. Question: How do I find the angles of a triangle if I know the lengths of all three sides?Īnswer: Use the cosine rule to find one of the angles. Use Pythagoras's theorem to work out remaining sideĪnd remaining angle = 180 - (90 + 26) = 64 degrees Length hypotenuse = length opposite side / sine (26 degrees) So sine (26 degrees) = length opposite side / length hypotenuse In your case, you know the side opposite the angle. Question: Which formula is used when given 90-degree triangle, opposite angle is 26 degrees and one leg is know?Īnswer: Use the fact that the cos of an angle is the length of the adjacent side divided by the hypotenuse, or the sine of an angle is the opposite side divided by the hypotenuse. However there is an infinite number of similar right triangles that have all three angles the same, so you need to know at least the length of one side. Question: How do you find the length of all the sides of a right triangle if all you know is Cos B is 0.75?Īnswer: You can find the angle B from the arccos of 0.75 and then use the fact that the three angles add up to 180 to find the remaining angle. The two equal sides are a and b and the angle between them is C Question: How do you find an angle of an isosceles if you only know two sides and the area?Īnswer: Let the triangle have sides of length a, b and c and angles A, B and C.
Similarly a/Sin A = c/Sin C and rearranging gives c = (a/Sin A)Sin C Add the sine, cosine and tan relationships between angles and the hypotenuse of the triangle to work out the remaining side. Question: How do I find the missing side of a triangle when only its height is known?Īnswer: Use Pythagoras's Theorem. Once you know that length, since the triangle is equilateral, you know the length of the other sides because all sides are of equal length. However, the length of at least one side must be known. Question: What is the formula for finding what an equilateral triangle of side a, b and c is?Īnswer: Since the triangle is equilateral, all the angles are 60 degrees. You need to know at least two angles and one side, or two sides and one angle, or one side and one angle if the triangle is a right-angled triangle. Question: How do I find the value if all three sides of a scalene triangle are unknown?Īnswer: If all the sides are unknown, you can't solve the triangle. You can prove this to yourself by drawing out the single side and angle and seeing how you can draw as many different shaped triangles as you want. So either one side and the two angles at each end or two sides and the angle between them. Question: How do you find the remaining sides of a triangle if you have only one angle and one side given?Īnswer: You need to have more information. This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional. Thes exception is if the known angle is in a rightangled triangle and not the right angle.Ģ. You need to know more information, either one other side or one other angle.
I know the length of a side and one angle Use the sine rule to work out the two unknown sides Sum of three angles is 180 degrees so remainging angle can be calculated. I know the length of a side and the angle at each end Use the cosine rule in reverse to work out each angle. Use the sine rule to work out the remaining sides. I know the length of one side and all three angles. Use the sine rule to work out remaining angles and side. I know the length of two sides and the angle opposite one of them. Use the cosine rule to work out remaining side and sine rule to work out remaining angles. I know the length of two sides and the angle between them. Use the trigonometric identities sine and cosine to work out the other sides and sum of angles (180 degrees) to work out remaining angle. Triangle is right and I know the length of one side and one angle Use Pythagoras's Theorem to work out remaining side and sine rule to work out angles. Triangle is right and I know length of two sides.
Isosceles triangle definition how to#
A summary of how to work out angles and sides of a triangle.