The converse of the Pythagorean Theorem is also true If a, b, and c are the lengths of sides of a triangle, and if a 2 b 2 c 2, then the triangle is a right triangle whose hypotenuse has length c. Applications to Triangles Discovering Geometry illustrates how to apply the Pythagorean Theorem to solve real-world problems. The following steps build on these actions so you can find all the solutions for this SSA problem Use the trig identity. to find the second angle of the second triangle. Because. subtract this value from 180 degrees to find that. Find the measure of the third angle. because the three angles must add to 180 degrees. Ex.1 If ABC is right angle triangle, B 90, AB 12 cm, AC 13 cm then find sin A and cos C. Sol. Using Pythagoras theorem B C A 12 AB 13 BC AC 2 AB 2 169 144 5 cm sin A AC BC 13 5 cos C AC AB 13 12 Ans. Ex.2 If sin A 2 1 in right triangle ABC, then find value of tan A, cosec A, tan B, cosec B. Sol. C B A 1 2 1 sin A 2 1.
The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan). These are
defined for acute angle below In these definitions, the terms opposite, adjacent, and hypotenuse refer to the lengths of the sides. A Given triangle is a right
angle triangle with PQ72 , PR7 & RQ7 Q B 25 Use the given right triangle to find ratios, in reduced form, for sin A, cos A, and tan A. 7 A A sinA(Opposite side to A)hypotenuse cosA(adjacent side to A)hypotenuse tanAsinAcosA. Right triangle PQR is shown below with the dimensions given in units. 13 12 R 5 o Which ratio has a value equal to 12 A cos(R) sin(P) B C sin(R) D. tan(P) O A B D ; Question Right triangle PQR