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QveST [7]
3 years ago
8

If a scalene triangle has its measures 4 m, 11 m and 8 m, find the largest angle.

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
3 0

Answer:

129.8 approximately

Step-by-step explanation:

So this sounds like a problem for the Law of Cosines. The largest angle is always opposite the largest side in a triangle.

So 11 is the largest side so the angle opposite to it is what we are trying to find. Let's call that angle, X.

My math is case sensitive.

X is the angle opposite to the side x.

Law of cosines formula is:

x^2=a^2+b^2-2ab \cos(X)

So we are looking for X.

We know x=11, a=4, and b=8 (it didn't matter if you called b=4 and a=8).

11^2=4^2+8^2-2(4)(8)\cos(X)

121=16+64-64\cos(X)

121=80-64\cos(X)

Subtract 80 on both sides:

121-80=-64\cos(X)

41=-64\cos(X)

Divide both sides by -64:

\frac{41}{-64}=\cos(X)

Now do the inverse of cosine of both sides or just arccos( )

[these are same thing]

\arccos(\frac{-41}{64})=X

Time for the calculator:

X=129.8 approximately

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Answer:

216°

Step-by-step explanation:

Both chords are the same length, so the left and right arcs are both 72°.  The whole circle is 360°, so:

72° + 72° + x = 360°

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The table shows the amount of money in your savings account over a period of 6
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A military aircraft can travel 740 miles per hour. The distance between Tyndall Air Force Base in Florida and Lakenheath Air For
BARSIC [14]

Answer: 3.5 h

Step-by-step explanation:

<u>1. Data:</u>

a) s = 740 miles / h

b) d = 2,567 miles

c) t = ?

<u>2. Equation:</u>

  • speed = distance / time
  • s = d / t

<u>3. Solution:</u>

  • Solve the equation for t:

        s = d / t ⇒ t = d / s

  • Substitute values:

        t = 2,567 miles / (740 miles/h) ≈ 3.47 h ≈ 3.5 h

   

5 0
3 years ago
Use the figure below to answer the questions.
Archy [21]

Answer:

a. What is the name of the 3D shape?

The name of the 3D shape is Prism

b. What is the formula for total surface area for this shape?

Total surface area:

S=2A_{b}+P_{b}h

c. What is the surface area of the figure?

The surface area of the figure is 144 cm²

Step-by-step explanation:

a. What is the name of the 3D shape?

The 3D shape has two congruent and parallel faces (triangles) and the other faces are parallelograms, then the 3D shape is a prism


b. What is the formula for total surface area for this shape?

Total Surface area:

S=2A_{b}+P_{b}h

where:

Area of the base of the prism: Ab

Perimeter of the base: Pb

Height of the prism: h


c. What is the surface area of the figure?

The base of the prism is a triangle. Then to calculate the area of the base, we must use the formula to calculate the area of a triangle:

A_{b}=\frac{bh}{2}\\ A_{b}=\frac{(4 cm)(3 cm)}{2}\\ A_{b}=\frac{12cm^{2} }{2}\\ A_{b}=6cm^{2}

The perimeter of the base is the perimeter of the triangle, equal to the sum of the sides of the triangle:

P_{b}=4cm+3cm+5cm\\ P_{b}=12cm

h: Height of the prism is the distance between the bases of the prism (the triangle), then h=11 cm

Then, replacing in the formula the known values:

S=2(6 cm^{2})+(12 cm)(11 cm)\\ S=12 cm^{2}+132 cm^{2}\\ S=144 cm^{2}


8 0
3 years ago
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