Question

The ratio of the legs of a right triangle is 19:28. Find the measurements of its angles.

Answer 1

θ (or x)=34.2° and 55.8°

or .597 and .974 radians

or 38 and 62 gradians

Explanation:

1.) Find the angles using the trigonometry, in this case I used a tan (opposite over adjacent)

so it should look like this

`tan(x)=((28)/(19) )`

2.) solve for θ by isolating it from tan

`(tan^(-1) )tan(x)=(28)/(19) (tan^-1)`

3.) use that to find the rest of the triangle's angles (if order for it to be a triangle, all angles must equal to 180° or
`\pi` radians, or 200 gradians )

so... (using degrees)

180°-90°-55.8°=34.2°