Question

12.) Solve the right triangle. Round answers to the nearest tenth. To receive full credit you must show all work. M 8 40° K L 2 Solve the right triangle Bound answers to the nearest tonth KL = ML = mZK =​

Answer 1

To solve the right triangle, we can use the trigonometric ratios sine, cosine, and tangent.

Given:

angle K = 40°

ML = 8

KL = 2

We can use the sine function to find the value of angle M:

sin(M) = KL / ML

sin(M) = 2 / 8

sin(M) = 0.25

So M = arcsin(0.25) = 14.04 (approximately)

Next, we can use the cosine function to find the value of MK:

cos(M) = ML / KL

cos(M) = 8 / 2

cos(M) = 4

So MK = 4

Lastly, we can use the tangent function to find the value of angle L:

tan(L) = KL / MK

tan(L) = 2 / 4

tan(L) = 0.5

So L = arctan(0.5) = 26.57 (approximately)

So the triangle is ML = 8, KL = 2, and angles M = 14.04° and L = 26.57° rounded to the nearest tenth.

Answer 2

Answer: KL = 6.1, MK = 5.2 and the angle mZK = 40.

Step-by-step explanation: In this problem, to solve for the remaining sides and angles of the triangle, we can use trigonometry.

First, let's use the sine function to find the value of KL:

sin(40) = KL/ML

KL = (sin(40))(ML)

KL = (sin(40))(8)

Next, let's use the cosine function to find the value of MK:

cos(40) = MK/ML

MK = (cos(40))(ML)

MK = (cos(40))(8)

Finally, let's use the tangent function to find the value of mZK:

tan(40) = KL/MK

mZK = tan(40)

To round the answers to the nearest tenth, we can use the function Math.round(x * 10) / 10 in Javascript.

sin(40) = 0.766

cos(40) = 0.644

tan(40) = 1.193

KL = (0.766)(8) = 6.128 ≈ 6.1

MK = (0.644)(8) = 5.152 ≈ 5.2

mZK = 1.193

So the triangle KL = 6.1, MK = 5.2 and the angle mZK = 40.