Question

How do I know which trigonometric ratio to use when given a problem?

Answer 1

There are three steps:
1. Choose which trig ratio to use.
Choose either sin, cos, or tan by determining which side you know and which side you are looking for.
2. Substitute
Substitute your information into the trig ratio.
3. Solve
Solve the resulting equation to find the length of the side.

Answer 2

1. Find b.
Step 1: Choose which trig ratio to use.
First, we know we must look at angle B because that is the angle we know the
measure of.(Now, you could find the measure of angle A and then use that but
that's less reliable since you could make a mistake.)
So, looking at angle B, we want to identify which sides are involved. We know
one side is 8m, and that side is adjacent to angle B. The side we're looking
for is opposite angle B. So we need to choose the trig ratio that has
opposite and adjacent. This of course is the tangent.

Answer 3

Step 2: Substitute
Next, we write our trig ratio:
\[\tan~B=\frac{ opp }{ adj }\]Then, we substitute in the angle
and the side we know:
\[\tan~B=\frac{ b }{ 8 }\]

Answer 4

Step 3: Solve
Now move the 8 to the other side
by multiplying both sides by 8:
And use a calculator to find the answer.
Well round to the nearest tenth: 3.7 m.