Question

A right-angled triangle has an angle of `28^circ` and a hypotenuse of `8` cm. What are the lengths of the other two sides?

Answer 1

The side have lengths of (approximately) 3.8 cm and 7.1 cm.
(See below for use of trigonometry to determine these values)

Explanation:

From the above:
`color(white)("XXX")"opposite " = sin(28^@)xx8" cm"`
(...using a calculator: `sin(28^@)=0.469472`)
So
`color(white)("XXX")"opposite" = 0.469472xx8" cm" = 3.755773" cm"`

`color(white)("XXX")"adjacent" = cos(28^@)xx 8 " cm"`
(...using a calculator: `cos(28^@)= 0.882948`)
So
`color(white)("XXX")"adjacent" = 0.882948xx8 " cm" = 7.063581 " cm"`