Question

A right triangle is shown. The hypotenuse has length b. The angle opposite to side a is y and the angle opposite to side c is x.
Which equations for the measures of the unknown angles x and y are correct? Check all that apply.

x = cos–1(StartFraction a Over c EndFraction)
x = sin–1(StartFraction c Over b EndFraction)
x = tan–1(StartFraction c Over a EndFraction)
y = sin–1(StartFraction a Over c EndFraction)
y = cos–1(StartFraction c Over b EndFraction)

Answer 1

Label sides: for angle x, opposite = c, adjacent = a, hypotenuse = b. So
- sin x = c/b, cos x = a/b, tan x = c/a.
For angle y, opposite = a, adjacent = c, hypotenuse = b. So
- sin y = a/b, cos y = c/b, tan y = a/c.

Therefore the correct equations are:
- x = sin⁻¹(c/b)
- x = tan⁻¹(c/a)
- y = cos⁻¹(c/b)

The other three are incorrect.