# 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.

Solution:

Redraw the triangle.

Find Y in triangle …II

Trigonometry says

 sin\ theta = (O)/H

Therefore

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

Find x now knowing 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

Solution:

Redraw the triangle

Find Y in triangle II

Trigonometry says

 sin\ theta = (O)/H

Therefore

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

Now find angle A in the triangle.

Trigonometry says

 sin\ theta = (O)/H

Therefore

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