Explanation:
To solve the equation (5r+7)tan47 = 137.2, we need to isolate the variable r. Let's break down the steps to find the solution.
Step 1: Distribute the tan47 to the terms inside the parentheses:
5rtan47 + 7tan47 = 137.2
Step 2: Simplify the equation:
5rtan47 = 137.2 - 7tan47
Step 3: Divide both sides of the equation by 5tan47 to isolate r:
r = (137.2 - 7tan47) / (5tan47)
Now, to find the numerical value of r, we need to substitute the value of tan47. The value of tan47 is approximately 1.0724.
r = (137.2 - 7 * 1.0724) / (5 * 1.0724)
Simplifying further:
r = (137.2 - 7.5072) / 5.362
r = 129.6928 / 5.362
r ≈ 24.18
Therefore, the solution to the equation (5r+7)tan47 = 137.2 is r ≈ 24.18.