For questions 38-40 use the triangle.
|\ 45° angles for the top of the
| \ triangle and the bottom right
| \C
| \ 38: If a=12, find b
| \ 39: If b=2,find c
| \ 40: If c=12,find a
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B. Is this pythagorean Therorem? When I try it that way it's not working out? Could someone please explain what to do. Thank you
So I assume this is a 90-45-45 triangle.
no, this is a 1-.707-.707 triangle.
I don'tknow where a, b, c are. For example, if the hypotenuse is 34, then the legs are 34*.707
If a leg were 15, then the hypotenuse would be 15/.707
Yes it's a 90, 45 45 triangle. And the letters go like this.
A
C
B
To solve the problem and find the missing values of b, c, and a, we need to use trigonometric functions, specifically the sine, cosine, and tangent.
38: Given that a = 12, we need to find b.
Since angle C is 45 degrees, we can use the sine function.
sin(C) = b / a
sin(45) = b / 12
To find b, multiply both sides by 12:
b = 12 * sin(45)
39: Given that b = 2, we need to find c.
Since angle C is 45 degrees, we can use the cosine function.
cos(C) = c / b
cos(45) = c / 2
To find c, multiply both sides by 2:
c = 2 * cos(45)
40: Given that c = 12, we need to find a.
Since angle C is 45 degrees, we can use the tangent function.
tan(C) = a / c
tan(45) = a / 12
To find a, multiply both sides by 12:
a = 12 * tan(45)
Now, let's calculate the missing values:
38: b = 12 * sin(45)
b ≈ 12 * 0.7071
b ≈ 8.485
39: c = 2 * cos(45)
c ≈ 2 * 0.7071
c ≈ 1.414
40: a = 12 * tan(45)
a ≈ 12 * 1
a ≈ 12
Therefore, b ≈ 8.485, c ≈ 1.414, and a ≈ 12.
Regarding your question about the Pythagorean theorem, it applies to right triangles, which have a right angle (90 degrees). In this triangle, angle C is not 90 degrees, so the Pythagorean theorem does not apply. Instead, we use trigonometric functions to solve for the missing side lengths.