Determine a , given that A = 63°, C = 49°, and c = 3. Round answers to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect.
a = 3.54, which can be rounded to a whole number 4.
a = 4
Oh, finding an angle using trigonometry! Let's have some fun with that!
To find angle A, we'll use the Law of Sines. It states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
Now, let's get our clown noses on and solve it!
The formula looks like this:
a/sin(A) = c/sin(C)
We know that C is 49° and c is 3. Plugging in these values, we get:
a/sin(A) = 3/sin(49°)
Cross-multiplying, it becomes:
a * sin(49°) = 3 * sin(A)
Now, let's divide both sides by sin(49°), and our equation looks like this:
a = (3 * sin(A)) / sin(49°)
Now, just plugging in A as 63°, we can calculate:
a = (3 * sin(63°)) / sin(49°)
Doing the calculations, we finally arrive at:
a ≈ 4
So, to round it to the nearest whole number, angle A is approximately 4 degrees.
And remember, always keep a sense of humor while doing math!
To find side a, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its corresponding angle is the same for all three sides and angles of the triangle.
Using the Law of Sines formula:
a/sin(A) = c/sin(C)
Plugging in the given values:
a/sin(63°) = 3/sin(49°)
To solve for a, we can cross-multiply and then solve for a.
a = (3 * sin(63°)) / sin(49°)
Using a calculator to evaluate the sine values:
a = (3 * 0.891) / 0.753
a = 3.984
Rounding to the nearest whole number:
a ≈ 4
Therefore, a is approximately 4.
the sides are in the same ratios as the sines of their opposite angles
a = c * [sin(A) / sin(C)]