Remark
There's a lot of points in this question. I'll try and give you complete answers.
"Page" One
Cos(42) = 0.7431
Most modern Calculators are answered this way.
Cos
42
=
And it should give you the answer I gave.
Question Two
Sin(42) = 2/3
There are 2 ways to find the cos(48).
1.
Just put it in your calculator. It gives you the same answer so cos(48) = 2/3
2.
The second way is to know that the sine of an angle and it's complement are equal. 0.66 is approximately equal to 2/3
Question 3
the same thing is true for tangents sort of.
Tan(20.5) = 1/tan(90 - 20.5)
Tan(20.5) = 1/tan(69.5) Let's see if that's right.
Tan(20.5) = 0.384 which is pretty close to 3/8
3/8 = 0.375
1/tan(69.5) = 0.374 same as above.
You would put this into your calculator as
1
divide
tan
69.5
=
So what you are intended to answer is Tan(69.5) = 8/3
"Page" Two
<A = 90 You just read that one. No calculator needed.
the easiest way to solve for angle B is to use the cos-1 of B
Cos(B) = adjacent / hypotenuse
Cos(B) = 14/32
The way you put this into your calculator is
2nd F [usually an orangy/yellow button]
cos-1
(
14
divide
32
)
=
Which should give you 64.06 degrees which must be rounded to the nearest degree = 64 degrees. Answer 1
Now the answer to the last angle = 180 - 90 - 64 = 26 degrees. Answer 2
"Page" Three
problem one
Make sure you use Cos-1
Cos-1(0.1045) = 84 degrees I'm being a little scant in my answer. you need to look back to find cos-1.
Problem two
Opposite = 93 meters (she's an awfully tall lady).
Angle = 26.3 degrees.
adjacent = ????
Tan(26.3) = opposite / adjacent
0.4942 = 93 / adjacent. Multiply both sides by adjacent
0.4942 * adjacent = 93 Divide by 0,4942
adjacent = 93/0.4942
adjacent = 188.2 meters away.
Concluding Comment
This is very long. Be patient with it. You'll learn quite a bit including when to round.