a. θ = 36. 9°
b. θ = 114. 2°
<h3>How to determine the value of theta</h3>
a. We use the cosine identity
cos θ = adjacent/hypotenuse
Adjacent = 4cm
Hypotenuse = 5cm
cos θ = 4/ 5
cos θ = 0. 8
Now, we have the inverse of the cosine value
θ = cos^-1 (0. 8)
θ = 36. 9°
b. We use the tangent identity
tan a = opposite / adjacent
tan a = 3. 8/1. 7
tan a = 2. 23
a = tan^-1 ( 2. 23)
a = 65. 8
We have;
a + θ = 180 °; angles on a straight line
θ = 180 - 65. 9
θ = 114. 2°
Learn more about trigonometric identities here:
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Answer:
448
Step-by-step explanation:
aₙ = a₁ + (n-1)d
a₈ = a₁ + (8-1)d = a₁ + 7d
a₁₂ = a₁ + 11d
a₈ + a₁₂ = 246 = 2a₁ + 18d a₁ + 9d = 123
a₁₀ + a₁₄ = a₁ + 9d + a₁ + 13d = 298 a₁ + 11d = 149
2d = 26
d = 13
a₁ = 6
a₃₅ = 6 + (35-1) x 13 = 448
Answer:
Step-by-step explanation:
Similar triangles
Cross multiply
2*(x+2) = 3*x
2x + 2*2 = 3x
2x + 4 = 3x
Subtract 2x from both sides
2x + 4 -2x = 3x - 2x
4 = x
x = 4
Answer:
a) t= 2hours and 10 minutes
b) t=4hours and 20 minutes
v1t1=v2t2
