Given An = 5a(n-1) where a1= 2. What are the first 4 terms
1 answer:
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Answer:
see explanation
Step-by-step explanation:
(1)
the sine of an angle =
(a)
here the opposite is 12 and the hypotenuse is 13
12 is the side opposite ∠DEF ← required angle
(b)
the tangent of an angle =
here the opposite is 5 and the adjacent is 12
∠DFE ← required angle
(2)
to calculate AB use Pythagoras' identity in the right triangle
AB² = 2² + 3² = 4 + 9 = 13, hence
AB = ≈ 3.6 ( to nearest tenth )
tanB = ⇒ B = 33.7°
tanA = ⇒ A = 56.3°
Answer:
The height of the hill = h = 580.7 feet
Step-by-step explanation:
Let height of the hill = h
From the triangle A B D
Tan 22 =
⇒ AB = h & B D = y + 700
⇒ Tan 22 = ------------(1)
From triangle ABC
Tan 38 =
⇒ AB = h & BC = y
⇒ Tan 38 = ------------------(2)
⇒ h = y tan 38 -----------------(3)
Put the value of h from equation (3) into equation (1) we get
⇒ (tan 22) × (y + 700) = y × tan 38
⇒ 0.40 y + 282.82 = y × 0.78
⇒ y = 742.12 feet -----------------(4)
Put this value of y in equation 3 we get
⇒ h = 742.12 × tan 38
⇒ h = 580.7 feet
This is the height of the hill.
