Solve the right triangle Find the length of the side opposit

Solve the right triangle. Find the length of the side opposite to the given angle. () Find the length of the side adjacent to the given angle. () Find the other acute angle. Find x rounded to one decimal place. Find x rounded to one decimal place. A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 30,000 ft. The pilot would like to estimate her distance from the Gateway Arch. She finds that the angle of depression to a point on the ground below the arch is 22 degree. (Round your answers to the nearest foot.) What is the distance between the plane and the base of the arch? What is the distance between a point on the ground directly below the plane and the base of the arch?

Solution

4.   sin theta=opposite/hypotenuse

opposite= hypotenuse * sin theta

opposite= 1000 sin 64=898.79

cos theta=adjacent/hypotenuse

adjacent=hypotenuse*cos theta

adjacent=1000*cos64=438.37

other acute angle=180-(90+64)=26 degree