Answer:
10. Not enough information
11. B ≈ 12.0°
12. A ≈ 34.1°
Step-by-step explanation:
10. Not enough information
11.
We need to use the Law of Sines, which states that for a triangle with lengths a, b, and c and angles A, B, and C:
Here, we can say that AB = c = 38, C = 128, and AC = b = 10. Plug these in to find B:
Solve for B:
B ≈ 12.0°
12.
Use the Law of Sines as above.
Solve for A:
A ≈ 34.1°
Answer:
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
In ΔAHD, the side opposite angle DAH is DH, and the hypotenuse is AD, so we have ...
sin(∠DAH) = DH/AD = 4/8
∠DAH = arcsin(4/8) = 30°
That makes ΔAHD a 30°-60°-90° triangle, so the side lengths have the ratios 1 : √3 : 2.
∠CAB = 2·30° = 60°, so ΔABC is also a 30°-60°-90° triangle having the same ratios of side lengths.
In short, ...
AH = √3·DH = 4√3
AC = 2·AH = 8√3
AB = 2·AC = 16√3
BC = √3·AC = 8·(√3)² = 24
Assuming the -3 is an exponent.
When the exponent is negative, it means to take the reciprocal then raise the denominator to the power.
So, -1/125 is the answer.
The statement that matches the vector operation shown on the coordinate grid is v + w = u.
<h3>How to add two vectors graphically?</h3>
In order to add two vectors a and b graphically by using the tail and tip method, we must draw the tail of b at the tip of vector a.
Then we must draw a line that goes from the tail of vector a to the tip of vector b.
This line represents the sum of a + b.
In the given problem, we notice that the tail of the vector w is on the tip of the vector v.
The line that joins the tail of vector v with the tip of vector w is vector u.
Therefore we can say that v + w = u
The statement that matches the vector operation shown on the coordinate grid is v + w = u.
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