This is a classic Pythagorean triangle. Although you have given the side lengths, you have NOT given a letter to correspond , with the given side. However, Let 12 be the adjacentr side (base) Let '5' be the opposite side ( perpendicular ) Let '13' by the hypotenuse. Sin(Angle) = opposite / hypotenuse = 5/13 Angle = Sin^(-1) 5/13 = 22.619... degrees. NB This is the angle between the hypotenuse and the base(adjacent) Now 'swopping' things around , we take the angle between the hypotenuse and the perpendicular (opposite) . This now becomes perpendicular(adjacent) and the base becomes the opposite. Hence Sin(angle) = 12/13 Angle = Sin^(-1) 12/13 = 67.380.... degrees. The angle at the 'top' of the triangle. Verification. ' 90 + 67.380... + 22.619... = 180 ( allow for calculator decimals).
To find the cosine of angle B given the sides of a triangle, you typically use the cosine rule or the relationship between the sides. However, the values "5," "13," and "12" seem to refer to the lengths of the sides of a triangle. If these correspond to a triangle with sides a = 5, b = 12, and c = 13, you can use the cosine rule: ( \cos(B) = \frac{a^2 + c^2 - b^2}{2ac} ). Plugging in the values, ( \cos(B) = \frac{5^2 + 13^2 - 12^2}{2 \cdot 5 \cdot 13} = \frac{25 + 169 - 144}{130} = \frac{50}{130} ), which simplifies to ( \cos(B) = \frac{5}{13} ).
Pythagoras. The right turn is assumed to be 90 degrees, and moving southwards. This forms the two shorter sides on a right angled triangle. They applying Pythagoras. h^)2) = 5^(2) + 12^(2) h^(2) = 25 + 144 h^(2) = 169 Don't forget to 'square root' both sides!!!! Hence h = sqrt(169) = 13 . This is a classic Pythagorean triangle.
Use Cosine Rule a^(2) = b^(2) + c^(2) - 2bcCosA Algebrically rearrange CosA = [a^(2) - b^(2) - c^(2)] / -2bc Substitute CosA = [13^(2) - 12^(2) - 5^(2)# / -2(12)(5) CosA = [ 169 - 144 - 25] / -120 Cos)A) = [0] / -120 CosA = 0 A = 90 degrees (the right angle opposite the hypotenuse)/ However, If 'A' is the angle between '12' & '13' then 'a' is the side '5' Hence (Notice the rearrangement of the numerical values). CosA = [5^(2) - 12^(2) - 13^(2) ] / -2(12)(13) CosA = [ 25 - 144 -169] / -312 CosA = [ -288[/-312 CosA = 288/312 A = Cos^(-1) [288/312] A = 22.61986495.... degrees.
add the
Yes because 12 divided by tan(67.38013505) equals 5 And: 122+52 = 169 making the hypotenuse of the right angle triangle 13 cm
The dimensions given fits that of a right angle triangle and sin^-1(12/13) = 67.38 degrees
tan(23) = 1.58815308
As given 51213 is just a number. However, a triangle with sides 5, 12, & 13, forms a classic Pythagorean right angled triangle.
Yes they do for a triangle using Pythagorean theorem 5 squared + 12 squared = 13 squared
Yes, because they comply with Pythagoras' theorem for a right angle triangle.
By Pythagorean theorem, if the sum of squares of smaller sides of a triangle equals the square of longest side, it is a right angle triangle where the long side is the hypotenuse. 5 squared plus 12 squared is equal to 13 squared
No because otherwise it would be a right angle triangle.
No because they don't comply with Pythagoras' theorem.
Tan(f) = HG/FG = 12/5 = 2.4
It is: cos = adj/hyp and the acute angles for the given right angle triangle are 67.38 degrees and 22.62 degrees
If the right angle is at A then SA = 5 mm.