Question

RAD is a 30°-60°-90° triangle. Determine the missing lengths.

Answer 1

DR = 10 units

AR = 8.66 units

Explanation:

By applying sine rule in the given right triangle,

sin(∠R) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

sin(30°) =
`(AD)/(DR)`

`(1)/(2)=(5)/(DR)`

DR = 10 units

By applying tangent rule in the given triangle,

tan(∠R) =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

`tan(30^0)=(AD)/(AR)`

`(1)/(√(3))=(5)/(AR)`

AR = 5√3

AR = 8.66 units