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:
x + y = 84
Step-by-step explanation:
Given
x : y : z = 5 : 1 : 3, then
= 5 ( multiply both sides by y )
x = 5y ←
and =
( cross- multiply )
3y = z
Substitute z = 3y into z - y = 28
3y - y = 28
2y = 28 ( divide both sides by 2 )
y = 14 ← ←
Substitute y = 14 into x = 5y
x = 5 × 14 = 70 ← ←
Substitute y = 14 into z - y = 28
z - 14 = 28 ( add 14 to both sides )
z = 42 ← ←
Thus x = 70, y = 14 and z = 42
Hence x + y = 70 + 14 = 84
