Right Triangle ABC has the following dimensions AB =6 , m∠A = 35° and m∠C = 90° . Find the other measurements of the triangle, AC , BC and m∠B . Show your work for all calculations. write in 2 sentences and write simple
Using the definition of sine, we can find AC by dividing the length of the side opposite angle A by the sine of angle A, giving us AC = 6/sin(35°) ≈ 10.97. BC can be found using the Pythagorean theorem, so BC = √(AC^2 - AB^2) = √(10.97^2 - 6^2) ≈ 9.43. Lastly, since the sum of angles in a triangle is 180°, m∠B = 180° - 35° - 90° = 55°. Thus, the other measurements of the triangle are AC ≈ 10.97, BC ≈ 9.43, and m∠B = 55°.
