# 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?

Apr 6, 2016

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: $\sin \left({28}^{\circ}\right) = 0.469472$)
So
color(white)("XXX")"opposite" = 0.469472xx8" cm" = 3.755773" cm"

color(white)("XXX")"adjacent" = cos(28^@)xx 8 " cm"
(...using a calculator: $\cos \left({28}^{\circ}\right) = 0.882948$)
So
color(white)("XXX")"adjacent" = 0.882948xx8 " cm" = 7.063581 " cm"