1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andre [41]
3 years ago
13

I need explanation for when to use the proper trig function in SOHCAHTOA and I need help and guidance for this question please

Mathematics
1 answer:
const2013 [10]3 years ago
4 0

Explanation:

For finding one missing side in a right triangle, the Pythagorean theorem is the tool of choice. Here, it tells you ...

  QR² = RS² + QS²

  QS = √(QR² -RS²) = √(18² -9²) = √243

  QS = 9√3 . . . . . as shown in your figure

___

The letters O, A, and H in SOH CAH TOA are references to the Opposite and Adjacent sides and the Hypotenuse. The opposite and adjacent sides are with respect to one of the acute angles in the triangle.

In your triangle QRS, the sides marked with lengths are QR (the hypotenuse) and RS. Side RS is adjacent to acute angle R, and opposite acute angle Q. If you want to use these side lengths to find the values of angles R and Q, you would use the SOH CAH TOA relations that involves the sides you have.

For angle R, you have A and H, so you use the cosine relationship:

  cos(R) = A/H = 9/18 = 1/2

You need to use your knowledge of the cosine function, or use the inverse cosine function on your calculator to find the angle:

  R = cos⁻¹(1/2) = 60°

__

Since you now know the value of angle R, you know that angle Q is 30° (the complement of 60°). If you want to use SOH CAH TOA to find it from the side lengths marked in the figure, you would choose the sine relationship. That is because you have the opposite side (RS) and the hypotenuse (QR).

  sin(Q) = opposite/hypotenuse = 9/18 = 1/2

Again, the inverse function (or your knowledge of sine function values) is needed:

  Q = sin⁻¹(1/2) = 30°

___

Of course, once you found the length QS, you have all three side lengths to choose from, so any of the trig functions could be used to find the acute angles:

  sin(R) = O/H = QS/QR = (9√3)/(18) = √3/2

  cos(R) = A/H = RS/RQ = 9/18 = 1/2

  tan(R) = O/A = QS/RS = (9/√3)/(9) = √3

__

  sin(Q) = O/H = RS/RQ = 9/18 = 1/2

  cos(Q) = A/H = QS/QR = (9√3)/(18) = √3/2

  tan(Q) = O/A = RS/QS = (9)/(9√3) = √3/3

__

The short answer is that you use the tool that makes use of the information you have available. If several possible tools can be used, you can choose the one that is easiest to use (requires the fewest computation steps, or makes use of rational, rather than irrational, numbers).

You might be interested in
Which statement describes the expression below? 1 + 6 ÷ 2 × 3 Multiply the quotient of 6 and 2 by 3, then add 1. Add 1 and 6, th
son4ous [18]

Answer:

Add 1 and 6, then divide by 2 and multiply by 3.

Step-by-step explanation:

5 0
3 years ago
Which best explains whether or not all isosceles triangles are similar? All isosceles triangles are similar. Two angles within e
Contact [7]
By Angle-Angle  simlilarity postulate :
If two angles of one triangle congruent to two angles of another, then triangles must be similar.
So, I think the answer is
<span>All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

Because two base angles in  </span>isosceles triangle are congruent, but it could be a lot of isosceles triangles that have different  congruent base angles.
 For example,
45-45-90 is an isosceles triangle, and 30-30-120 is an isosceles triangles, but they do not have 2 congruent angles.
7 0
3 years ago
Whats the answer? Please respond ASAP!
Artemon [7]

Answer:

C.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
The graph shows a proportional relationship between the cups of flour a baker uses and the number of cookies made.
algol13

Answer:

Step-by-step explanation:

(0,0)A baker doesn't use any cups of flour so he can't make any cookies

(1,18)A baker uses 1 cup of flour and makes 18 cookies

8 0
3 years ago
Read 2 more answers
Demetrius invested money into two different stocks after one year he revived a letter that summarized the preformance of the sto
tino4ka555 [31]

Answer:

C

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Zacharias is using the quadratic formula to solve the equation 0 = –2x2 5x – 3. he begins by substituting as shown.quadratic for
    10·2 answers
  • A fair dice is rolled. Work out the probability of getting a factor of 12.
    15·2 answers
  • What problem led to playgrounds becoming more common in America cities
    10·1 answer
  • Select the true statement about the series, ¾ + 7/8 + 11/12 + 15/16…
    9·1 answer
  • Find m Find m Find m Find m
    6·2 answers
  • Jared uses 24 tiles to cover the top of his desk. Of the 24 tiles 3_8 are blue. How many of the tiles are blue?
    5·1 answer
  • Which function is the inverse of F(x) = b^x?<br> HELP FAST
    5·1 answer
  • Help me!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    7·1 answer
  • 7over10 subtract 5over12 in simplest form
    5·1 answer
  • Out of 1,500 licensed drivers, 900 admitted that they do not like to drive at night. What is the 92% confidence interval for the
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!