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e-lub [12.9K]
3 years ago
7

A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, whic

h takes the ball back to the starting point. What angles are formed by these tosses. Step by Step explanation.. Please
Mathematics
1 answer:
Rainbow [258]3 years ago
4 0

angles formed by these tosses are  79.45, 59.02 and 41.53 degrees to the nearest hundredth.

<u>Step-by-step explanation:</u>

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

c^2 = a^2 + b^2 - 2ab (cosx)

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒ c^2 = a^2 + b^2 - 2ab (cosx)

⇒ c^2 -a^2 - b^2 = -2ab (cosx)

⇒ (cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}

⇒ (cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}

⇒ (cosx) =0.18310

⇒ cos^{-1}(cosx) = cos^{-1}(0.18310)

⇒ x = 79.45

The Law of Sines (or Sine Rule) is very useful for solving triangles:

\frac{a}{sin A} = \frac{ b}{sin B} =  \frac{c}{sin C}

We can now find another angle using the sine rule:

⇒\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}

⇒sin Y = \frac{(7.5 (sin 79.45))}{  8.6}

⇒Y = 59.02 degrees

So, the third angle =180 - 79.45 - 59.02 = 41.53 degrees.

Therefore, angles formed by these tosses are  79.45, 59.02 and 41.53 degrees to the nearest hundredth.

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