Question

solve the right triangle.
b = □°□ (round to the nearest integer as needed.)
a = □ m (round to the nearest integer as needed.)
b = □ m (round to the nearest integer as needed.)

Explanation:

Step1: Find angle B

In a right - triangle, the sum of the two non - right angles is 90°. Given angle A = 30°26', convert 30°26' to decimal degrees. 26' = 26/60 ≈ 0.433°, so A≈30.433°. Then B = 90°−A. B = 90° - 30°26'= 59°34'.

Step2: Find side a

Use the sine function. sin(A)=a/c, where c = 966 m. So a = c×sin(A). a = 966×sin(30°26'). Since sin(30°26')≈sin(30.433°)≈0.507, a = 966×0.507≈489 m.

Step3: Find side b

Use the cosine function. cos(A)=b/c, where c = 966 m. So b = c×cos(A). b = 966×cos(30°26'). Since cos(30°26')≈cos(30.433°)≈0.862, b = 966×0.862≈833 m.

Answer:

B = 59°34'
a = 489 m
b = 833 m