Solving for angle of a triangle?

The unknown side = _/(27 x 27) - (25.6 x 25.6) because the square on a hypotenuse equals the square on the other two sides.

Dividing this answer by the base gives the Tangent of that angle, which is found by standard tables.

You are given the hypotenuse h (opposite the right angle) and the base b.

Considering the angle A between the hypotenuse and the base, b is adjacent.

The relevant trig function is cos A = adjacent / hypotenuse = b / h

But we need the angle, in other words the angle A whose cos is b / h. This is the inverse cos or arccos.

A = arccos b / h = arccos 25.6 / 27 = arccos 0.948 = 18.56 degrees

You did not aspect out that your hypotenuse 10 runs in the course of the middle of the circle, subsequently, it turns into the diameter of the circle. if it quite is so, variety a radius from the middle of the circle to the point the position both factors of the circle's legs intersect. in view that your hypotenuse 10 runs via the middle, 0.5 of it truly is 5 (radius) and the line from the middle to the intersecting factors of the legs is likewise 5 ! consequently, utilising the Pythagorean Th c^2 = a^2 + b^2, that'll be c = SqRt of 5^2 + 5^2 c = SqRt of 50 or c = 5 SqRt of two (genuinely, it is between both chords ! Checking, Hypotenuse = 10^2 = (SqRt 50)^2 + (SqRt50)^2 10^2 = 50 + 50 10 = SqRt one hundred 10 = 10 !!! Proving that the answer's authentic. And that each chords has a length of SqRt 50 !

opposite side = 8.58 inches

angle = 18.53 degrees

Pythagorean Theorem: c² = a² + b²

sin θ = opposite/hypotenuse = a/c

18 degrees, 32 minutes

approximately 18.53 degrees