Draw a model for a fraction1/6
2 answers:
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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.
<u>Given</u>:
Given that the triangles ABD and CAD are similar.
The length of AB is 12.
The length of BD is x.
The length of AC is 27.
We need to determine the value of x.
<u>Value of x:</u>
Let us use the leg rule to determine the value of x.
Thus, we have;
Substituting the values, we get;
Cross multiplying, we get;
Dividing both sides by 27, we have;
Thus, the value of x is
Hence, Option D is the correct answer.