The distance to the nearest gas station is 2 3/4 miles what is this distance written as a decimal
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Problem 1
Since point P is the tangent point, this means angle OPT is a right angle
angle OPT = 90 degrees
Let's use the Pythagorean theorem to find the missing side 'a'
a^2 + b^2 = c^2
a^2 + 7^2 = 12^2
a^2 + 49 = 144
a^2 = 144 - 49
a^2 = 95
a = sqrt(95)
a = 9.7467943
a = 9.7
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Let's use the sine and arcsine rule to find angle y
sin(angle) = opposite/hypotenuse
sin(y) = 7/12
y = arcsin( 7/12 )
y = 35.6853347
y = 35.7
The value of y is approximate. Make sure your calculator is in degree mode. Arcsine is the same as inverse sine or
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Problem 2
Focus on triangle OHP. This may or may not be a right triangle. The goal is to test if it is or not.
We use the converse of the Pythagorean theorem to check.
Recall that the converse of the Pythagorean theorem says: If a^2+b^2 = c^2 is a true equation, then the triangle is a right triangle. The value of c is always the longest side. The order of a and b doesn't matter.
In this case we have
- a = 7
- b = 13
- c = 16
Which leads to
a^2 + b^2 = c^2
7^2 + 13^2 = 16^2
49 + 169 = 256
218 = 256
We get a false equation at the end, since both sides aren't the same number, which means the original equation is false.
We don't get a^2 + b^2 = c^2 to be true, therefore this triangle is not a right triangle.
Consequently, this means angle OPH cannot possible be 90 degrees (if it was then we'd have a right triangle). Therefore, point P is not a tangent point.
You follow the same basic idea for triangle OQH and show that point Q is not a tangent point either. Or you could use a symmetry argument to note that triangle OPH is a mirror reflection of triangle OQH over the line segment OH. This implies that whatever properties triangle OPH has, then triangle OQH has them as well for the corresponding pieces.
The scale factor is: 1/5.
The missing sides of figure B are: 2.4, 3.6, and 4.
<h3>How to find Scale Factor?</h3>Scale factor = dimension of new figure / dimension of original figure
The polygons given are shown in the diagram attached below.
Figure A is the original figure
Figure B is the new figure.
x, y, and z has been used to mark the missing sides of figure B.
One dimension of original figure = 15
Corresponding dimension of the new figure = 3
Scale factor = new/original = 3/15
Scale factor = 1/5
To find the missing sides of figure B, multiply each corresponding side lengths of Figure A by the scale factor:
x = 12 × 1/5 = 2.4
y = 18 × 1/5 = 3.6
z = 20 × 1/5 = 4
In summary:
The scale factor is: 1/5.
The missing sides of figure B are: 2.4, 3.6, and 4.
Learn more about scale factor on:
