Final answer:
To solve the right triangle △ABC, calculate angle B using the fact that the angles in a triangle sum to 180°, and then use trigonometry to find the lengths of sides a and b by applying the cosine and sine functions to angle A and the hypotenuse c.
Step-by-step explanation:
To solve the right triangle △ABC with the given measurements, where ∠C=90°, ∠A=35° 23′, and hypotenuse c measures 490.4 feet, we begin by finding ∠B using the fact that the sum of angles in a triangle is 180°. Since ∠C is 90° and ∠A is 35° 23′, we can calculate ∠B as:
∠B = 180° - 90° - 35° 23′ = 54° 37′
Next, we use the trigonometric ratios to find the lengths of sides a and b. For side a (adjacent to ∠A), we have:
a = c * cos(∠A) = 490.4 * cos(35° 23′)
Similarly, for side b (opposite ∠A):
b = c * sin(∠A) = 490.4 * sin(35° 23′)
Calculating these will give the lengths of sides a and b in feet.