Two forces of $30 \mathrm{~N}$ (newtons) and $50 \mathrm{~N}$ act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the smaller force.
The magnitude of the resultant is $\square$ Newtons.
(Round to the nearest integer as needed.)
The angle the resultant makes with the smaller force is $\square^{\circ}$.
(Round to the nearest integer as needed.)
Answer
Again, we need to round this to the nearest integer, so the angle the resultant force makes with the smaller force is \(\boxed{59^{\circ}} \).
Step 1 ：Given two forces of magnitudes 30 N and 50 N acting at right angles to each other.
Step 2 ：We can find the magnitude of the resultant force using the Pythagorean theorem, which gives us \( \sqrt{30^2 + 50^2} \approx 58.31 \) N.
Step 3 ：However, we need to round this to the nearest integer, so the magnitude of the resultant force is \(\boxed{58} \) N.
Step 4 ：We can find the angle the resultant force makes with the smaller force using the tangent function, which gives us \( \tan^{-1}(\frac{50}{30}) \approx 59.04 \) degrees.
Step 5 ：Again, we need to round this to the nearest integer, so the angle the resultant force makes with the smaller force is \(\boxed{59^{\circ}} \).
