Examples NOT using sine rule

If the following questions came up in the exam we recommend using LOGIC to work out how to solve this problem using standard trigonometry (SOH CAH TOA) and Pythagoras.

Example 1

Find the length of `x` in the following diagram.

Example 1 first find the length of X

Solution:

Redraw the triangle.

Step 1 redraw the triangle

Find Y in triangle …II

Step 2 find Y in the triangle

Trigonometry says

`sin\ theta`

`=`

`(O)/H`

Therefore

`sin80^@`	`=`	`Y/7`
`Y`	`=`	`7sin80^@`

Find `x` now knowing Y.

Step 3 find X when you know Y

Trigonometry says

`sin\ theta`

`=`

`(O)/H`

Therefore

`sin60^@`	`=`	`(7sin80^@)/x`
`x`	`=`	`(7sin80^@)/(sin60^@)`
`x`	`=`	`6.893/0.866`
`x`	`=`	`7.959`

Example 2

Find angle A

Example 2 find A in the triangle

Solution:

Redraw the triangle

Step 1 redraw the triangle

Find Y in triangle II

Step 2 find Y in the triangle

Trigonometry says

`sin\ theta`

`=`

`(O)/H`

Therefore

`sin63^@`	`=`	`Y/4.8`
`Y`	`=`	`4.8sin63^@`

Now find angle A in the triangle.

Step 3 Now find the result of A

Trigonometry says

`sin\ theta`

`=`

`(O)/H`

Therefore

`sinA`	`=`	`(4.8sin63^@)/5.7`
`sinA`	`=`	`4.276/5.7`
`sinA`	`=`	`0.75`
`A`	`=`	`48.61^@`