In a right triangle one of the perpendicular side is one less than 2 times the smaller side. Hypotenuse is one more than 2 times the same smaller side. By taking the smaller side as x cm write the algebraic expression of the sequence and compute all three sides of the right triangle
Answers
Answer:
Right Triangles
Let’s agree again to the standard convention for labelling the parts of a right triangle. Let the right angle be labelled C and the hypotenuse c. Let A and B denote the other two angles, and a and b the sides opposite them, respectively.
Right triangle with parts standardly labelled
Solving right triangles
We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts.
Pythagorean theorem: a2 + b2 = c2.
Sines: sin A = a/c, sin B = b/c.
Cosines: cos A = b/c, cos B = a/c.
Tangents: tan A = a/b, tan B = b/a.
Let’s first look at some cases where we don’t know all the sides. Suppose we don’t know the hypotenuse but we do know the other two sides. The Pythagorean theorem will give us the hypotenuse. For instance, if a = 10 and b = 24, then c2 = a2 + b2 = 102 + 242 = 100 + 576 = 676. The square root of 676 is 26, so c = 26. (It’s nice to give examples where the square roots come out whole numbers; in life they usually don’t.)
Now suppose we know the hypotenuse and one side, but have to find the other. For example, if b = 119 and c = 169, then a2 = c2 – b2 = 1692 – 1192 = 28561 – 14161 = 14400, and the square root of 14400 is 120, so a = 120.
We might only know one side but we also know an angle. For example, if the side a = 15 and the angle A = 41°, we can use a sine and a tangent to find the hypotenuse and the other side. Since sin A = a/c, we know c = a/sin A = 15/sin 41. Using a calculator, this is 15/0.6561 = 22.864. Also, tan A = a/b, so b = a/tan A = 15/tan 41 = 15/0.8693 = 17.256. Whether you use a sine, cosine, or tangent depends on which side and angle you know.