Question

The two shorter sides of a right triangle have the same length. The area of the right triangle is 6.55 square meters. What is the length of the hypotenuse? c= meters Two of the interior angles of a triangle are 54.6 degrees and 82.2 degrees. What is the third interior angle of the triangle? θ= degrees In a right triangle, the side opposite angle θ has length 5.13 meters and the hypotenuse has length 7.70 meters. What is the sine of the angle? sinθ=

Answer 1

The hypotenuse of the right triangle is approximately 5.13 meters. The third interior angle of the triangle is 43.2 degrees. The sine of the angle in the right triangle is approximately 0.67.

Step-by-step explanation:

The right triangle with equal shorter sides can be seen as two 45-45-90 right triangles together. In such a triangle, the length of the hypotenuse is √2 times the length of each of the equal sides. To find the side length, use the formula that the area of a triangle is 1/2 * base * height. Given that the area is 6.55 square meters, the length of each equal side a can be calculated as √(2*6.55) ≈ 3.63 meters. Therefore, the hypotenuse c is 3.63 * √2 ≈ 5.13 meters.

The sum of the interior angles of a triangle is always 180 degrees. If one angle is 54.6 degrees and the other is 82.2 degrees, then the third interior angle θ can be found as 180 - 54.6 - 82.2 = 43.2 degrees.

In a right triangle, the sine of the angle θ is defined as the ratio of the length of the side opposite θ to the length of the hypotenuse. Thus, sin(θ)=5.13/7.70 ≈ 0.67.

Learn more about Triangle Calculations