exam 9
question 1: standard g.srt.6
what is theta?
a. a constant
b. the angle the trig ratio is based on
c. change in y over change in x
d. the coordinate plane
question 2: standard g.srt.6
what does soh stand for in soh cah toa?
a. sine = opposite over hypotenuse
b. cosine = opposite over hypotenuse
c. sine = tangent over adjacent
d. tangent = opposite over adjacent
question 3: standard g.srt.6
what does cah stand for in soh cah toa?
a. sine = opposite over hypotenuse
b. cosine = opposite over hypotenuse
c. cosine = adjacent over hypotenuse
d. tangent = opposite over adjacent
question 4: standard g.srt.6
what does toa stand for in soh cah toa?
a. cosine = adjacent over hypotenuse
b. sine = opposite over adjacent
c. tangent = opposite over adjacent
d. tangent = adjacent over opposite
question 5: standard g.srt.6
solve for the missing side using tangent.
image of a right triangle with one leg 8, one leg z, and one acute angle 35°
a. x= 11.42
b. x= 5.3
c. x= 47.8
d. x = 33.2

Question

exam 9
question 1: standard g.srt.6
what is theta?
  a. a constant
  b. the angle the trig ratio is based on
  c. change in y over change in x
  d. the coordinate plane
question 2: standard g.srt.6
what does soh stand for in soh cah toa?
  a. sine = opposite over hypotenuse
  b. cosine = opposite over hypotenuse
  c. sine = tangent over adjacent
  d. tangent = opposite over adjacent
question 3: standard g.srt.6
what does cah stand for in soh cah toa?
  a. sine = opposite over hypotenuse
  b. cosine = opposite over hypotenuse
  c. cosine = adjacent over hypotenuse
  d. tangent = opposite over adjacent
question 4: standard g.srt.6
what does toa stand for in soh cah toa?
  a. cosine = adjacent over hypotenuse
  b. sine = opposite over adjacent
  c. tangent = opposite over adjacent
  d. tangent = adjacent over opposite
question 5: standard g.srt.6
solve for the missing side using tangent.
image of a right triangle with one leg 8, one leg z, and one acute angle 35°
  a. x= 11.42
  b. x= 5.3
  c. x= 47.8
  d. x = 33.2

Accepted Answer

### Question 1
# Brief Explanations:
Theta in trigonometry is the angle the trigonometric ratio is based on. Option a is incorrect as theta is a variable (angle), not a constant. Option c is the definition of slope, not theta. Option d is incorrect as theta is an angle, not the coordinate plane.
# Answer:
b. The angle the trig ratio is based on

### Question 2
# Brief Explanations:
SOH in SOH CAH TOA stands for Sine = Opposite over Hypotenuse. Option b is incorrect (cosine is not opposite over hypotenuse), option c is incorrect (sine is not tangent over adjacent), option d is the definition of tangent, not SOH.
# Answer:
a. Sine = opposite over hypotenuse

### Question 3
# Brief Explanations:
CAH in SOH CAH TOA stands for Cosine = Adjacent over Hypotenuse. Option a is sine's definition, option b is incorrect (cosine is not opposite over hypotenuse), option d is tangent's definition.
# Answer:
c. Cosine = adjacent over hypotenuse

### Question 4
# Brief Explanations:
TOA in SOH CAH TOA stands for Tangent = Opposite over Adjacent. Option a is cosine's definition, option b is incorrect (sine is not opposite over adjacent), option d is incorrect (tangent is not adjacent over opposite).
# Answer:
c. Tangent = opposite over adjacent

### Question 5
# Explanation:
## Step1: Recall the tangent ratio
The tangent of an angle in a right triangle is defined as $	an(	heta) = \frac{	ext{opposite}}{	ext{adjacent}}$. In the given right triangle, the angle is $35^\circ$, the opposite side to the angle is $8$ (assuming the vertical side is opposite), and the adjacent side is $z$ (the horizontal side we need to find? Wait, no, wait. Wait, maybe the vertical side is 8, and we need to find the adjacent side? Wait, no, let's check the triangle. The right angle, the angle of $35^\circ$, the side opposite to $35^\circ$ is 8, and the adjacent side is $z$? Wait, no, tangent is opposite over adjacent. Wait, maybe the angle is $35^\circ$, the opposite side is 8, and we need to find the adjacent side? Wait, no, wait, maybe the vertical side is 8 (opposite to the angle), and the horizontal side is $z$ (adjacent). Wait, $	an(35^\circ) = \frac{8}{z}$? No, wait, no. Wait, maybe the angle is $35^\circ$, the adjacent side is $z$, and the opposite side is 8. Wait, $	an(35^\circ) = \frac{	ext{opposite}}{	ext{adjacent}} = \frac{8}{z}$? No, that would be if 8 is opposite. Wait, no, maybe the angle is $35^\circ$, the adjacent side is $z$, and the opposite side is 8. So $	an(35^\circ) = \frac{8}{z}$? Then $z = \frac{8}{	an(35^\circ)}$. Wait, but $	an(35^\circ) \approx 0.7002$. So $z = \frac{8}{0.7002} \approx 11.42$? Wait, no, wait, maybe I got opposite and adjacent wrong. Wait, maybe the vertical side is $z$ and the horizontal side is 8? No, the triangle has a right angle, one angle 35 degrees, the vertical side is 8 (let's say), and the horizontal side is $z$. So the angle of 35 degrees is at the bottom, so the opposite side is 8 (vertical), adjacent is $z$ (horizontal). So $	an(35^\circ) = \frac{8}{z}$? Then $z = \frac{8}{	an(35^\circ)}$. Wait, $	an(35^\circ) \approx 0.7002$, so $z = \frac{8}{0.7002} \approx 11.42$. Wait, but the options are a. x=11.42, b. x=5.3, c. x=47.8, d. x=33.2. Wait, maybe I mixed up opposite and adjacent. Wait, maybe the angle is 35 degrees, the adjacent side is 8, and the opposite side is $x$? Wait, no, the question says "solve for the missing side using tangent". Let's re-express. Let's assume the angle is $35^\circ$, the adjacent side is $z$ (horizontal), and the opposite side is 8 (vertical). Then $	an(35^\circ) = \frac{8}{z} \implies z = \frac{8}{	an(35^\circ)}$. Calculating $	an(35^\circ) \approx 0.7002$, so $z \approx \frac{8}{0.7002} \approx 11.42$, which is option a. Wait, but the option is x=11.42, maybe the variable is x instead of z. So the missing side is x=11.42.
## Step2: Calculate the value
We know that $	an(35^\circ) \approx 0.7002$. If $	an(35^\circ) = \frac{8}{x}$ (assuming x is the adjacent side), then $x = \frac{8}{	an(35^\circ)} \approx \frac{8}{0.7002} \approx 11.42$.
# Answer:
a. x= 11.42

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