Question

Find each measure measurement indicated. Round your answers to the nearest tenth. Please show work​

Answer 1

#1: The measure of m<B is 125°.

#2: M<Y is equal a 27°.

#3: So the length of DF is 5.99 km.

#4: the side length AC is 13.1 feet.

Step-by-step explanation:

# 1: The following given,

c = AB = 17 cm

a = BC = unknown

b = CA = 44 cm

Ø = 125

M<B means it is the angle at vertex B of the triangle, it is also the only angle given in thbe figure.

Therefore, The measure of m<B is 125°.

#2: We can calculate the value of the angles by means of the law of sine which is the following:

`(yz)/(sin \: x) = (xz)/(sin \: y) = (xy)/(sin \: z)`

We need you know the Y value, therefore we replace and solve for Y

`(xz)/(sin \: y) = (xy)/(sin \: z) \\ (5)/(sin \: y) = (11)/(sin \: 88) \\ 5 \: . \: sin \: 88 = 11 \: . \: sin \: y \\ sin \: y = (5 \: . \: sin \: 88)/(11) \\ sin \: y = 0.45426 \\ y = {sin}^( - 1) (0.45426) \\ y = 27`

#3: In order to find the length of Df, we can use the law of sines in this triangle:

`(11)/(sin \: (103)) = (df)/(sin \: (32)) \\ (11)/(0.974) = (df)/(0.53) \\ df = (11.0.53)/(0.974) \\ df = 5.99`

So the length of DF is 5.99 km.

#4: We are given two two angles and one side length.

<A = 37°

<B = 65°

AB = 13 ft

We are asked to find side length AC

We can use the "law of sines" to find the side length AC

`(sin \: c)/(ab) = (sin \: b)/(ac)`

Let us first find the angle <C

Recall that the sum of all three interior angles of a triangle must be equal to 180°

`< a + < b + < c = 180 \\ 37 + 65 + < c = 180 \\ 102 + < c = 180 \\ < c = 180 - 102 \\ < c = 78`

So, the angle <C is 78°

Now let us substitute all the known values into the law of sines formula and solve for AC

`(sin \: c)/(ab) = (sin \: b)/(ac) \\ (sin \: 75)/(13) = (sin \: 65)/(ac) \\ ac = (sin \: 65 \: . \: 13)/(sin \: 75) \\ ac = (9.06 \: . \: 13)/(0.899) \\ ac = 13.1ft`

Therefore, the side length AC is 13.1 feet.

Answer 2

9514 1404 393

Answer:

1. ∠B = 125°
2. ∠y = 27°
3. DF = 6 km
4. AC = 12 ft

Step-by-step explanation:

1. The desired angle is given on the diagram as 125°.

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For the rest of these problems, the Law of Sines applies. A side can be found from ...

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

and an angle can be found from ...

A = arcsin(a/b·sin(B))

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2. Y = arcsin(y/z·sin(Z)) = arcsin(5/11·sin(88°))

∠Y = 27°

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3. DF = (11 km)·sin(32°)/sin(103°)

DF = 5.98 km ≈ 6 km

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4. b = c·sin(B)/sin(C) = (13 ft)·sin(65°)/sin(180° -65° -37°)

b = 12 ft