Question

Given |u| = 10 at ∠135° and |v| = 5 at ∠30°, what expression can be used to find |u + v|?

(10)2 + (5)2 – 2(10)(5) cos(45°)
(10)2 + (5)2 – 2(10)(5) cos(75°)
(10)2 + (5)2 – 2(10)(5) cos(105°)
(10)2 + (5)2 – 2(10)(5) cos(165°)

Answer 1

its B

Explanation:

Just got it right on edge

Answer 2

B,
`10^(2) + 5^(2)- 2(10)(5)cos(75)`

Explanation:

Using the law of cosines, which is
`c^(2)=a^(2)+b^(2)-2ab cos(C)`, you can simply insert all the values.

c=|u+v|

a= r value of u (10)

b= r value of v (5)

To find C, you simply have to subtract v from u, and then subtract that number from 180 to find the reference angle.

I.E.: ∠135 - ∠30 = ∠105 ↔ 180 - 105 = 75 = C

so, the completed equation would be 10^{2} + 5^{2}- 2(10)(5)cos(75)