Please help me with my Trigonometry?

a) b = 25sin25 = 10.57

b) a = 25cos25 = 22.66

You know that angle B is 25 degrees and that angle C is 90 degrees. This means that Angle A must be 65 degrees. Since we know each angle, finding the length of each side can be easily done with the following:

sin(theta) = opposite/hypotenuse

cos(theta) = adjacent/hypotenuse

tan(theta) = opposite/adjacent

These are important, and you should remember them.

Now you can take angle B to find the other sides and angles.

For example, use sin(theta) = opposite/hypotenuse.

When you plug it all in, you will get:

sin(25 degrees) = b / 25

Doing some algebra, you can re-write this as:

b = 25sin(25)

So now we know what the length of side b is 10.57.

I am not certain what exactly the question means by, "three different ways", but my guess would be the following three ways:

cos(25) = a / 25

tan(25) = 10.57 / a

a^2 + 10.57^2 = 25^2

1.

Consider the given right triangle ABC:

tan 25 = b/a

a^2 + b^2 = 625

Solution:

a ≈ 22.6577, b ≈ 10.5655

(a)

Find the length of side b to two decimal places.

b ≈ 10.57

(b)

Find the length of side a to two decimal places.

a ≈ 22.66