Question

the hypotenuse of a right triangle is 10cm and one angle is 45°.what is its area​

Answer 1

Step-by-step explanation:let, ∆ abc be a right angled triangleHypotenuse (ac) = 10 cm - given let, angle a = 45° and angle b = 90°therefore, angle (a) + angle (b) + angle (c) = 180° -angle sum property of a triangletherefore, 45+90+ angle (c) = 180° 135 + angle (c) = 180°angle (c) = 180 - 135angle (c) = 45°therefore, ∆ abc is an 45°-45°-90° trianglebase bc = 1/√2 × hypotenuse -side opposite to 45°base bc= 1/√2×10 = 5√2similarly, height ab = 5√2area of ∆ abc = 1/2 × base × height = 1/2 × 5√2 ×5√2 =1/2 × 25× 2 = 1/2× 50 =25 sq.cm