How do I do this?

Question

Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.

c = 16,    ∡ A = 45°

a=?

b=?

Answer 1

As c is the hypotenuse and angle A is 45, angle C must be 90, and angle B must be 45.

So you have a special right triangle with angles 45-45-90. If the two legs are x then the hypotenuse is x√2.

So you know x√2 = 16, so x = 16 / √2. Multiplying top and bottom by √2 gives 16√2 / 2 = 8√2.

So a, b are both 16/√2 = 8√2