CPM Homework Help : PC Problem 10-74

Given vector $\textbf{v} = \langle 4,3 \rangle$ and vector $\textbf{u} = \langle a , 5 \rangle$ , what must the value of $a$ be in order for the angle between the two vectors to equal $60°$ ?

Hint:

Review the Math Notes box on Dot Product in Lesson 10.1.4.

Step 1:

$\cos 60^º =\frac{4a+3(5)}{\left( \sqrt{3^2+4^2} \right)\left( \sqrt{a^2+5^2} \right) }$

Step 2:

$\cos 60º=\frac{4a+15}{5\sqrt{a^2+25}}$

Now continue solving on your own.