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3 years ago

In ΔKLM, the measure of ∠M=90°, the measure of ∠L=18°, and KL = 8.3 feet. Find the length of MK to the nearest tenth of a foot.

Mathematics

1 answer:

const2013 [10]3 years ago

7 0

Answer:

2.6 ft

Step-by-step explanation:

8.3/sin 90 = MK/sin 18

MK = 8.3 sin 18 / sin 90

MK = 2.6 ft

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2 years ago

A boat is pulled toward a dock by means of a rope wound on a drum that is located 6 ft above the bow of the boat. If the rope is

Monica [59]

Answer:

Step-by-step explanation:

Given that:

The height of the dock (h) = 6

Let represent d to be the distance between the boat and the dock

Let the length of the rope between the boat and the drum be denoted by (l)

Then, the rate of change for the length of the rope be:

dl/dt = -5 ft/s

Using Pythagoras rule to determine the relationship between these values, we have:

$l^2 = h^2 +d^2$

$l^2 = 6^2 + d^2$

$l^2 = 36 + d^2$

We relate to: $2l * \dfrac{dl}{dt} = 2d* \dfrac{dd}{dt}$

From the question;

l = 34,

So to find $\dfrac{dd}{dt}$ , we get;

$d = \sqrt{l^2 - 36}$

$d = \sqrt{34^2 - 36}$

$d = \sqrt{1156- 36}$

$d = \sqrt{1120}$

d = 33.46

So, we have:

$\dfrac{dd}{dt}= \dfrac{l}{d} \times \dfrac{dl}{dt}$

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4 0

2 years ago

Please Help ASAP!!!!

KIM [24]

Answer:

$m\angle M = 98\degree$

Step-by-step explanation:

As we know that:

Sum of the measure of all interior angles of a triangle is always 180°.

$\therefore (3x-16)\degree+(x+6)\degree+ x\degree = 180\degree\\\therefore (5x-10)\degree = 180\degree\\5x-10 = 180\\5x = 180 + 10\\5x = 190\\x= \frac{190}{5}\\x= 38\\\because m\angle M = (3x-16)\degree\\\therefore m\angle M = (3\times 38 -16)\degree\\\therefore m\angle M = (3\times 38 -16)\degree\\\therefore m\angle M = (114 -16)\degree\\\therefore m\angle M = 98\degree$