For a given right triangle, side a = 76.4 feet and side b = 39.3 feet. What is the measure of angle A to the nearest degree?
To find the measure of angle A in a right triangle, you can use trigonometric functions. In this case, you're provided with the lengths of the two sides adjacent to angle A: side a and side b.
To determine the measure of angle A, you need to use the inverse trigonometric function called tangent (tan). The formula to find angle A is:
A = atan(a/b)
Here's how you can calculate it step by step:
1. Substitute the given values into the formula: A = atan(76.4/39.3).
2. Use a calculator or a math software that has inverse trigonometric functions. Find the arctan (inverse tangent) of the ratio: tan^(-1)(76.4/39.3).
3. Evaluate the expression: A ≈ 63.53 degrees.
Therefore, the measure of angle A in the given right triangle is approximately 64 degrees.