Question

Find the missing side lengths. Answers are in simplest radical form with the denominator rationalized

Answer 1

`m = 5 √(3)`

`n = 5`

Explanation:

Given

The triangle above

Required

Find the missing lengths

The missing lengths can be calculated by applying trigonometry ratios

From the triangle above,

the Hypotenuse is 10

Angle = 60

Calculating m

The relationship between m, the Hypotenuse and angle 60 is defined as follows;

`sin \theta = (Opp)/(Hyp)`

Where
`\theta = 60`

`Opp = m`

`Hyp = 10`

The above formula becomes

`sin60= (m)/(10)`

Multiply both sides by 10

`10 * sin60= (m)/(10) * 10`

`10 * sin60= m`

In radical from,
`sin60 = (√(3))/(2)`

`10 * sin60= m` becomes

`10 * (√(3))/(2)= m`

`(10* √(3))/(2)= m`

`5 √(3)= m`

`m = 5 √(3)`

Calculating n

The relationship between n, the Hypotenuse and angle 60 is defined as follows;

`cos\theta = (Adj)/(Hyp)`

Where
`\theta = 60`

`Adj = n`

`Hyp = 10`

The above formula becomes

`cos60= (n)/(10)`

Multiply both sides by 10

`10 * cos60= (n)/(10) * 10`

`10 * cos60= n`

In radical from,
`cos60= (1)/(2)`

`10 * cos60= n` becomes

`10 * (1)/(2)= n`

`(10*1)/(2)= n`

`5 = n`

`n = 5`