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Nataly [62]
4 years ago
9

Using the triangle pictured, find the measure of side AB. Round your answer to the nearest tenth. A) 1.6 B) 2.2 C) 2.7 D) 3.3

Mathematics
1 answer:
Yuki888 [10]4 years ago
6 0

Answer:

Option B (AB = 2.2 units).

Step-by-step explanation:

The diagram shows that there are two sides given and one angle is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:

sin ABC / AC = sin BAC / BC.

Plugging ABC=72 degrees, AC=2.5, and BC=2.1 in the sine rule gives:

sin 72 / 2.5 = sin BAC / 2.1.

Cross multiplying gives:

sin BAC = (2.1*sin 72)/2.5.

sin BAC = 0.79888747368.

Taking sin inverse on both sides gives:

BAC = arcsin (0.79888747368) = 53.0239949 degrees.

To find AB, first, the angle ACB is required. To find that angle, use the triangular law of angles. All the three angles sum up to 180 degrees. Therefore ACB = 180 - 72 - 53.0239949 = 54.9760051  degrees.

Now applying the Sine Rule to find AB:

sin ACB / AB = sin ABC / AC.

sin (54.9760051) / AB = sin 72 / 2.5.

AB = (2.5*sin (54.9760051))/sin (72) = 2.2 (to the nearest tenth).

Therefore, AB = 2.2 units, i.e. Option B!!!

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7 0
3 years ago
I need to turn this in in 2 hours please hurry
Nuetrik [128]

Answer:

  2) 162°, 72°, 108°

  3) 144°, 54°, 126°

Step-by-step explanation:

1) Multiply the equation by 2sin(θ) to get an equation that looks like ...

   sin(θ) = <some numerical expression>

Use your knowledge of the sines of special angles to find two angles that have this sine value. (The attached table along with the relations discussed below will get you there.)

____

2, 3) You need to review the meaning of "supplement".

It is true that ...

  sin(θ) = sin(θ+360°),

but it is also true that ...

  sin(θ) = sin(180°-θ) . . . . the supplement of the angle

This latter relation is the one applicable to this question.

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Similarly, it is true that ...

  cos(θ) = -cos(θ+180°),

but it is also true that ...

  cos(θ) = -cos(180°-θ) . . . . the supplement of the angle

As above, it is this latter relation that applies to problems 2 and 3.

6 0
3 years ago
f the length of side a is 12 centimeters, m= 36°, and m= 75°, what is the length of side b? Round your response to two decimal p
-Dominant- [34]

Answer:

Option C. is correct

Step-by-step explanation:

In the triangle ABC, vertices are A(12, 8), B(4, 8) and C(4, 14)

AB =

BC =

AC =

In triangle XYZ vertices are X(6,6), Y(4,12) and Z(10, 14)

XY =

YZ =

XZ =

In triangle MNO, vertices are M(4, 16), N(4, 8) and O(-2, 8)

MN =

MO =

NO =

In triangle JKL, vertices are J(14, -2), K(12,2) and L(20, 4)

JK =

KL =

JL =

Now we compare the sides for the congruence

Since AB = MN = 8

BC = NO = 6

AC = OM = 10

So ΔABC ≅ Δ MNO

Option C. is correct

Read more on Brainly.com - brainly.com/question/1747695#readmore

3 0
3 years ago
SOMEONE PLEASE HELP ME 3/4(x+4)=1/4(x+8)
Troyanec [42]

Answer:

x=-2

Step-by-step explanation:

To solve this equation, we can use PEMDAS or Order of Operations.

Parenthesis

Exponents

Multiplication>Division

Addition>Subtraction

Using the various properties can also help make the equation easier.

First, solve for parenthesis using the distributive property.

Our equation is now : 3/4x+3=1/4x+2

Now, subtract 2 on both sides, to cancel out the positive 2 on the right.

3/4x+1=1/4x

Now subtract 3/4x from both sides.

1=-2/4x

Finally, to isolate x, divide both sides by -2/4

1/-2/4=-2

x=-2

Hope this helps!

5 0
3 years ago
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max2010maxim [7]

Answer:

No idea

Step-by-step explanation:

3 0
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