Answer:
7.8m 110.2°
Step-by-step explanation:
A suitable calculator can tell you the sum in polar or rectangular coordinates. Alternatively, you can compute the vector components and add those. The sum can be then converted to polar form, if you wish.
Calculator result
The first attachment shows the result from a TI-84 work-alike app.
x +y = 5m 60° +6m 150° ≈ 7.8m 110.2°
In rectangular coordinates, that is ...
x +y ≈ (-2.696, 7.330)
Vector components
Even if you compute the sum "by hand," you still need a calculator for the trig functions.
x = 5m(cos(60°), sin(60°)) ≈ (2.500, 4.330)m
y = 6m(cos(150°), sin(150°)) ≈ (-5.196, 3.000)m
Then the sum is ...
x +y = (2.500-5.196, 4.330+3.000)m = (-2.696, 7.330)m
The angle in polar coordinates is the second-quadrant angle ...
∠r = arctan(y/x) = arctan(7.330/-2.696) ≈ 110.2°
The magnitude of the resultant is ...
|r| = √(x² +y²) = √((-2.696)² +7.330²) ≈ 7.810
x +y ≈ 7.810m 110.2°
Additional ccomment
You may notice that the given vectors are at right angles to each other. That means the magnitude of the resultant can be found using the Pythagorean theorem. It will be ...
√(5²+6²) = √61 ≈ 7.810.
The angle will be the original angle of x plus the larger angle in the right triangle:
60° +arctan(6/5) ≈ 110.2°
You can see this in the vector diagram of the second attachment.