In ΔKLM, l = 26 cm, k = 56 cm and ∠K=22°. Find all possible values of ∠L, to the nearest degree.

Answers

Answer 1

Answer:

10 degrees

Step-by-step explanation:

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Answer 2

The possible value of ∠L in ΔKLM is approximately 22 degrees.

What is geometry?

Geometry is the study of two-dimensional and three-dimensional figures such as quadrilaterals, triangles, circles, their sides, and angles.

A square triangle is a diagram made by using the squares and the triangle simultaneously. Here in the image below you can see we can make the square triangle by using one square and three triangles.

To find the possible values of ∠L in triangle ΔKLM, we can use the Law of Cosines, which relates the sides and angles of a triangle:

c² = a²+ b²- 2abcos(C)

Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.

In our case, we know that:

KL = l = 26 cm (the side opposite to ∠M)

KM = k = 56 cm (the side opposite to ∠L)

∠K = 22° (angle opposite to KL)

To find the length of LM (the side opposite to ∠K), we can use the Law of Cosines:

LM² = KL² + KM^2 - 2KLKMcos(K)

LM² = 26² + 56² - 2(26)(56)cos(22°)

LM ≈ 61.3 cm

Now we can use the Law of Sines, which relates the lengths of the sides and the opposite angles of a triangle:

a/sin(A) = b/sin(B) = c/sin(C)

In our case, we can use this formula to find the value of sin(∠L):

sin(∠L)/KM = sin(∠K)/LM

sin(∠L)/56 = sin(22°)/61.3

sin(∠L) ≈ 0.374

∠L ≈ arcsin(0.374)

∠L ≈ 22° (rounded to the nearest degree)

Therefore, the possible value of ∠L in ΔKLM is approximately 22 degrees.

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The distances they jumped were

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