Solve $\frac{4}{r}=\cos 43^{\circ}$
Give your answer to 2 d.p.
Answer (1)
Rearrange the equation to isolate r : r = c o s 4 3 ∘ 4 .
Calculate cos 4 3 ∘ ≈ 0.73135 .
Substitute the value into the equation for r : r = 0.73135 4 ≈ 5.4693 .
Round to 2 decimal places: 5.47 .
Explanation
Understanding the Problem We are given the equation r 4 = cos 4 3 ∘ and we want to solve for r , giving the answer to 2 decimal places.
Isolating r First, we rearrange the equation to isolate r . Multiplying both sides by r gives 4 = r cos 4 3 ∘ . Then, dividing both sides by cos 4 3 ∘ gives us r = cos 4 3 ∘ 4 .
Calculating cosine Next, we need to find the value of cos 4 3 ∘ . The result of this calculation is approximately 0.73135.
Finding r Now, we substitute this value back into the equation for r : r = 0.73135 4 ≈ 5.4693 .
Rounding to 2 d.p. Finally, we round the value of r to 2 decimal places, which gives us r ≈ 5.47 .
Examples
Imagine you are building a ramp that needs to rise to a certain height over a specific distance. If the angle of elevation of the ramp is 43 degrees, and you want the horizontal distance covered by the ramp to be 4 meters, you can use this calculation to determine the length of the ramp needed. This type of problem helps in construction, engineering, and even in designing accessible spaces.
