Maria and Katy each have a piece of string. When they put the two pieces of string together end to end, the total length is 84in
1 answer:
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Answer:
x = 100°
Step-by-step explanation:
p and q are parallel lines. Construct line 'l' parallel to p and q
a = 30° {p// l when parallel lines are intersected by transversal alternate interior angles are congruent}
c +110 = 180 {linear pair}
c = 180 - 110
c = 70°
b= c {q // l when parallel lines are intersected by transversal alternate interior angles are congruent}
b = 70°
x = a + b
x = 30° + 70°
x = 100°
Step-by-step explanation:
<h3>Need to FinD :</h3>- We have to find the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0.
Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.
Where,
- PQ = Opposite side
- QR = Adjacent side
- RP = Hypotenuse
- ∠Q = 90°
- ∠C = θ
As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,
Since, we know that,
- cosθ = 5/13
- QR (Adjacent side) = 5
- RP (Hypotenuse) = 13
So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.
Therefore,
∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.
Where,
- Opposite side = 12
- Hypotenuse = 13
Therefore,
Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.
- By substituting the values, we get,
∴ Hence, the required answer is 17/7.
