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brilliants [131]
3 years ago
5

What was the distance of the ship from its starting point

Mathematics
1 answer:
tresset_1 [31]3 years ago
8 0
A^2+B^2=C^2
18^2+80^2=C^2
324+6400=C^2
6724=C^2
*Squareroot*
82=C
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How do you get the range?​
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[7, -8)

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2 years ago
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The triangle below is equilateral. Find the length of side x to the nearest tenth.
Gemiola [76]

Answer:

\sqrt{\frac{15}{2} } or 2.738

Step-by-step explanation:

Let’s just look at the triangle on the top with the \sqrt{10} on the top and x on the bottom. (Basically the top half to the equilateral triangle)

There is a small square in the bottom right corner, which indicates that this triangle is a right triangle. This means that we can use the Pythagorean Theorem: a^{2} +b^{2} =c^{2}

We know that \sqrt{10} is our hypotenuse, and therefore our c in our equation. Let’s say that x=a in our equation. Therefore we are left to find b. However, b is half the length of the side of the original equilateral triangle. An equilateral triangle means that all three sides are the same length. Therefore our side would also be \sqrt{10} units long. However we know that b is half of that value, so b=\frac{1}{2}(\sqrt{10}) or \frac{\sqrt{10} }{2}

Plugging these values into the equation:

x^2+ (\frac{\sqrt{10} }{2})^{2}=\sqrt{10} ^{2}

x^{2}=\sqrt{10} ^{2}-\frac{\sqrt{10} }{2} ^{2}

x^{2} =10-\frac{10}{4}

x^{2} =\frac{15}{2}

x=\sqrt{\frac{15}{2} }

This approximately equals 2.738

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2 years ago
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Are the following triangles similar? Justify your answer.
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Yes they are similar.

There are three similarity criteria for triangles.

The first one (AAA) , your case, says that two triangles are similar if their corresponding angles are equal.

The second one (SAS) says that two triangles are similar if two sides have lengths in the same ratio and the angles that are included in these two sides are equal.

The third one (SSS) says that two triangles are similar of all of their sides have lengths in the same ratio.

About the first criteria, you actually need only two corresponding angles to be the same, because the third will always be the difference between 180° and the two angles.

Remember that you CANNOT exceed 180° for the sum of the three angles of a triangle.

And remember also that similarity involves correspondence in sides and angles. Two triangles, with same angles, but mirrored, are not similar!

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