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sattari [20]
3 years ago
6

Find the value of x​

Mathematics
1 answer:
KATRIN_1 [288]3 years ago
3 0

Answer:

Step-by-step explanation:

Here we have the length of the hypotenuse (16) and that of the vertical leg (11).  The cosine function inputs this data:

            adjacent side                11

sin x = -----------------------  =  ----------------  =  0.6875

              hypotenuse                 16

We find x using the arccos function:  arccos 0.6875 = 0.81 radians or

                                                                                          46.57 degrees

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Two circles with different radii have chords AB and CD, such that AB is congruent to CD. Are the arcs intersected by these chord
emmainna [20.7K]

The arcs intersected by these chords are not congruent.

Given that two circles with different radii have chords AB and CD, such that AB is congruent to CD.

Let r₁ and r₂ be the radii of two different circles with centers O and O' respectively.

Assuming that the each of the ∠АОВ  and ∠CO'D is less than or equal to π.

Then, we have isosceles triangle AOB and CO'D such that,

AO = OB = r₁,

CO' = O'D = r₂,

Let us assume that r₁< r₂;

We can see that arc(AB) intersected by AB is greater than arc(CD), intersected by the chord CD;

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Indeed,

arc(AB) = r₁ angle (AOB)

arc(CD) = r₂ angle (CO'D)

So, we have to prove that ;

∠AOB >∠CO'D       ......(2)

Since each angle is less than or equal to π, and so

∠AOB/2  and ∠CO'D/2 is less than or equal to π

it suffices to show that :

tan(AOB/2) >tan(CO'D/2) ......(3)

From triangle AOB :

tan(AOB/2) = AB/(2*r₁)

tan(CO'D/2) = CD/(2*r₂)

Since AB = CD and r₁ < r₂ (As obtained from the result of (3) ), therefore, arc(AB) > arc(CD).

Hence, for two circles with different radii have chords AB and CD, such that AB is congruent to CD but the arcs intersected by these chords are not congruent.

Learn more about congruent from here brainly.com/question/1675117

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