Answer:
Y = 32.7°
Step-by-step explanation:
We will apply the Cosine law in the given triangle XYZ,
x = 90 ft
y = 55 ft
z = 50 ft
We have to find the measure of angle Y.
y² = x² + z² - 2xzCosY
(55)² = (90)² + (50)² - 2(90)(50)cosY
3025 = 8100 + 2500 - 9000.cosY
9000.cosY = 10600 - 3025
cosY =
= 0.84167
Y =
Y = 32.68 ≈ 32.7°
Therefore, measure of angle Y = 32.7°
Answer:
(a) 105°
(b) 75°
(c) 105°
Step-by-step explanation:
According to the options, we have,
(a) The car is travelling west on the 4th street and turns towards south on King Avenue.
So the angle (a) will be the angle made by the car's turning.
As, ∠(a) + 75° = 180°
i.e. ∠(a) = 180° - 75°
i.e. ∠(a) = 105°
(b) The car is travelling southwest on the King Avenue and turns right onto 3rd street.
So the angle (b) will be the angle made by the car's turning.
As, 3rd and 4th street are parallel. So, the corresponding angles have equal measures.
Thus, ∠(b) = 75°
(c) The car is travelling northeast on the King Avenue and turns right onto 4th street.
So the angle (c) will be the angle made by the car's turning.
As, ∠(c) + 75° = 180°
i.e. ∠(c) = 180° - 75°
i.e. ∠(c) = 105°
