Question

A triangle has sides A, B, and C. The angle between sides A and B is `(pi)/2` and the angle between sides B and C is `pi/12`. If side B has a length of 27, what is the area of the triangle?

Answer 1

`Area triangle = 97.66`

Explanation:

Name the angles between sides`A and B` is
`color(red)(angleM)`
Name the angles between sides`B and C` is
`color(brown)(angleN)`

GIVEN:
`color(red)(angleM=pi/2)`
`color(brown)(angleN=pi/12)`
side`B=27`

Let us find the area of this triangle:
The given `triangle` is right at M because `color(red)(angleM=pi/2)`

`color(blue)(Area=(b*h)/2)`
so,
base `color(blue)b=B=27`
height `color(blue)h=color(green)A=???`

`color(blue)(Area=(27*color(green)A)/2)`

Let us find side `color(green)A=???`
side `A` is opposite to `color(brown)(angleN)`
Since given the adjacent side `B` to the angle `color(brown)(angleN)`

`color(purple)(tanN=A/B)`
`tan(pi/12)=A/B`
`tan(pi/12)=A/27`
`A=tan(pi/12)*27`

`color(green)(A=7.235)`

Therefore,
`color(blue)(Area=(27*color(green)A)/2)`
`color(blue)(Area=(27*color(green)7.235)/2)`
`color(blue)(Area=97.66)`