Question

Can anybody can help me how to solve this trigonometry problem?

Answer 1

`"Side a"=10.817`
`"Side c"=13.634`
`"Angle B"=37.5^@`

Explanation:

I'm assuming that Angle C is `90^@`, even though it is not marked as such.

You can find Side a and Side c using the trigonometric ratios. As you may or may not have been taught:

`"Sine"="Opposite"/"Hypotenuse"`

`"Cosine"="Adjacent"/"Hypotenuse"`

`"Tangent"="Opposite"/"Adjacent"`

Or as I like to think of it: `"SOH"` `"CAH"` `"TOA"`

Since we know Angle A, and we know Side b (the non-Hypotenuse side that is adjacent to the angle), we can figure out the other sides.

If Side b is the "Adjacent" side, Side c is the Hypotenuse and Side a is the "Opposite" side. Using that information:

`tan(A)="Side a"/"Side b"`

`cos(A)="Side b"/"Side c"`

`tan(52.5^@)="Side a"/8.3 rArr 8.3xxtan(52.5^@)="Side a"`

`cos(52.5^@)=8.3/"Side c" rArr 8.3/cos(52.5^@)="Side c"`

`color(red)("Side a"=10.817`

`color(blue)("Side c"=13.634`

Finally, we have Angle B. We know that the sum of the internal angles of a triangle comes to `180^@`. Since we know Angle A and Angle C, we can subtract them from the total to get Angle B.

`/_A+/_B+/_C=180^@`

`52.5^@+/_B+90^@=180^@ rArr /_B+142.5^@=180^@`

`color(green)(/_B=37.5^@`