Question

Consider ΔABC, where ∠C = 90° and ∠A + ∠B = 90°. Click on the statements that are true about the relationships of the angles Angles A and B are complementary angles. If sin A ≈ 0.766, then sin B ≈ 0.766. If sin A ≈ 0.766, then cos B ≈ 0.766. If cos B ≈ 0.766, then the sin A ≈ 0.766,

Answer 1

Answer: Angles A and B are complementary angles

If Sin A ≈ 0.766 then Cos B ≈ 0.766.

If Cos B ≈ 0.766 then Sin A ≈ 0.766

Step-by-step explanation: In any given right angled triangle, one angle measures 90 degrees while the addition of the other two angles equals to 90 degrees. Hence if angle C is given as 90 degrees, then angles A and B added together equals 90 degrees (complementary angles equal 90 degrees).

Also, Sin A cannot be the same value as Sin B, since angle A and angle B are not equal in measurement. However, being complementary, the Sin of angle A equals the Cos of angle B.

If Sin A ≈ 0.766, then angle A ≈ 50 degrees

That makes angle B equal to 40 degrees. The Cos of B ≈ 0.766

Therefore if Sin A ≈ 0.766, then Cos B ≈ 0.766

If Cos B ≈ 0.766 then Sin A ≈ 0.766 are both correct