Solving triangles and Solving logarithms

By: Jesse Samuel

Solving Logarithms

Logarithmic formula : logbasey = x

Exponential form : y = b^x

As you can see they are very similar

When solving for x you can move the base value to the other side, like this!

log216 = x is equivalent to 2^x = 16

Then you make the bases the same so you can cancel them

2^x = 2^4, Now you can set the exponents equal to each other and solve! --> x = 4

Now try some out on your own!

a) x = log1/3 27

b) x = log64 1/32

c) 3 = log x 125

(Answers: -3, -1/3, 5)

Solving Triangles

The angles always add to 180

A + B + C = 180 When you know two angles you can find the third angle Law of Sines : a/sin A = b/sin B = c/sin C When there is an angle opposite a side, this equation comes to the rescue.

Law of Cosines : c^2 = a^2 + b^2 - 2abcos (C) It is an enhanced version of the Pythagoras Theorem that works

on any triangle. With those three equations you can solve any triangle 

TIPS: When the triangle has a right angle, then use it, that is usually much simpler.

When two angles are known, work out the third using Angles of a Triangle Add to 180°.

Try The Law of Sines before the The Law of Cosines as it is easier to use.

Now you try some !

84.3 8

5 33.5

9 62.2

a/sin A = 8/sin(62.2°) = 80.885

answer= 9.04



b/sin B = 5/sin(33.5°) = 50.552 

answer = 9.06

c/sin C = 9/sin(84.3°) = 90.995

answer = 9.05