Question

Where do I start to solve this problem? do I calculate the altitude or use pythagorean theorem?

Answer 1

As shown in the image:

There are two right triangles:

the triangle are similar

naming the points for easy calculation

measure of the angle zyw = measure of the angle yxw

And the measure of the angle ywz = measure of the angle xwy

So, the triangle WYZ will be similar to the triangle WXY

So, the corresponding side will be in proportion

`\begin{gathered} (wy)/(wx)=(wz)/(wy) \\ (a)/(16)=(4)/(a) \\ a^2=4\cdot16=64 \\ a=\sqrt[]{64}=8 \end{gathered}`

In the right triangle ywz:

using Pythagorean theorem:

`\begin{gathered} yz^2=yw^2+wz^2 \\ b^2=a^2+4^2=8^2+4^2=64+16=80 \\ b=\sqrt[]{80}=8.94 \end{gathered}`