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
True [87]
3 years ago
14

Solve △PQR. Round function values to 4 decimal places. Round final answers to the nearest tenth.

Mathematics
1 answer:
mestny [16]3 years ago
4 0

Answer:

The length of q is 7.6 units

The measure of angle R is 31.9°

The measure of angle P is 66.1°

Step-by-step explanation:

Let us use the sine and cosine rules to solve the triangle

In Δ PQR,

p is the opposite side to ∠P

q is the opposite side to ∠Q

r is the opposite side to ∠R

∵ p = 7 units

∵ r = 4 units

∵ m∠Q = 82°

- Angle Q is between p and r so let us find q using cosine rule

∵ q² = p² + r² - 2(p)(r) cos(∠Q)

- Substitute the values of p, r and ∠Q in the rule

∴ q² = (7)² + (4)² - 2(7)(4) cos(82°)

∴ q² = 49 + 16 - 56 cos(82°)

∴ q² = 57.2063

- Take √  for both sides

∴ q = 7.5635

- Round it to the nearest tenth

∴ The length of q is 7.6 units

Now let us use the sine rule to find the measures of ∠R and ∠P

∵ \frac{q}{sin(Q)}=\frac{r}{sin(R)}=\frac{p}{sin(P)}

- Let us find sin(R)

∴  \frac{7.5635}{sin(82)}=\frac{4}{sin(R)}

- By using cross multiplication

∴ 7.5635 × sin(R) = 4 × sin(82)

∴ 7.5635 sin(R) = 4 sin(82)

- Divide both sides 7.5635

∴ sin(R) = 0.5285

- Use sin^{-1} to find m∠R

∵ m∠R = sin^{-1} (0.5285)

∴ m∠R = 31.9042

- Round it to the nearest tenth

∴ The measure of angle R is 31.9°

∵ The sum of the measures of the interior angles of a Δ is 180°

∴ m∠P + m∠Q + m∠R = 180°

∴ m∠P + 82 + 31.9 = 180

∴ m∠P + 113.9 = 180

- Subtract 113.9 from both sides

∴ m∠P = 66.1°

∴ The measure of angle P is 66.1°

You might be interested in
Can someone help me and explain? I will mark brainlest. ♡
Sedbober [7]

Answer:

p'(4) = -3

q'(8) = \frac{1}{4}\\

Step-by-step explanation:

For p'(4):

p(x) = f(x)g(x) \\ p'(x) = \frac{d}{dx}(f(x)g(x)) \\ p'(x) = f'(x)g(x) +f(x)g'(x)

p'(4) = f'(4)g(4) + f(4)g'(4) \\ p'(4) = (-1)(3) +(7)(0) \\ p'(4) = -3

For q'(8):

q(x) = \frac{f(x)}{g(x)} \\ q'(x)= \frac{d}{dx}(\frac{f(x)}{g(x)}) \\ q'(x) = \frac{f'(x)g(x) -f(x)g'(x)}{{g(x)}^2}

q'(8) = \frac{f'(8)g(8) -f(8)g'(8)}{{g(8)}^2} \\ q'(8) = \frac{(2)(2) -(6)(\frac{1}{2})}{{2}^2} \\ q'(8) = \frac{4 -3}{4} \\ q'(8) = \frac{1}{4}

4 0
3 years ago
Read 2 more answers
Twice the difference of a number + -3 is 4 find the number
NNADVOKAT [17]

Answer:

The number is 5

Step-by-step explanation:

If we need to find the hidden number, Which for simplicity's sake we will denote as "n", lets first write out the equation.

"2 x [n + (-3)] = 4"

We can work through this problem backwards. if we need two times the sum of "n" and (-3) to get to 4, the only number that can be multiplied by 2 to get a product of 4 is 2, so "n" + (-3) must equal 2. so, From here, we can figure out that since 5 + (-3) equals 2, "n" Must equal 5. so, if we plug in 5 for "n" the equation looks like this:

"2 x [5 + (-3)] = 4"

So, since the equation makes sense, the answer is, "n = 5"

7 0
3 years ago
I’m having trouble finding the answer
Viefleur [7K]
Could never be me lol
6 0
3 years ago
Construct 3 linear equation starting with qiven solution z = 1/3
Andreyy89

Answer:

(a)9z+2=5

(b)21z-11=-4

(c)4z=2-2z

Step-by-step explanation:

We are required to construct 3 linear equations starting with the given solution z = 1/3.

<u>Equation 1</u>

<u />z=\frac{1}{3}<u />

Multiply both sides by 9

9z=\frac{1}{3}\times 9\\9z=3

Rewrite 3 as 5-2

9z=5-2

Add 2 to both sides

Our first equation is: 9z+2=5

<u>Equation 2</u>

<u />z=\frac{1}{3}<u />

Multiply both sides by 21

21z=\frac{1}{3}\times 21\\21z=7

Rewrite 7 as 11-4

21z=11-4

Subtract 11 from both sides

Our second equation is: 21z-11=-4

<u>Equation 3</u>

<u />z=\frac{1}{3}<u />

Multiply both sides by 6

6z=\frac{1}{3}\times 6\\6z=2

Rewrite 6z as 4z+2z

4z+2z=2

Subtract 2z from both sides

Our third equation is: 4z=2-2z

4 0
3 years ago
Subtract 55 from the sum of 243 and 8
Igoryamba

Answer:

the answer is 196

243+8=251

251-55=196

Step-by-step explanation:

hope this helps plz mark brainiest :)

8 0
3 years ago
Other questions:
  • What is the x to this line?
    15·1 answer
  • If x and y vary directly, and x = 10 when y = 3, what will be the value of x when y = 9?
    9·2 answers
  • If the relation is a function, list the domain and range. If the relation is not a function, choose "not a function".
    8·1 answer
  • Solve for d.<br> d•3/10=1/4
    15·2 answers
  • How many significant digits are in 80,000
    8·2 answers
  • Please help!!!! No explanation needed <br> Help is appreciated
    8·1 answer
  • I need help with this I will I’ve you Brainiest if right
    7·1 answer
  • Help plz i give brainiest
    9·2 answers
  • Ty-qy+p=r solve for y ​
    6·1 answer
  • Z varies directly as x^3 and inversely as y^3. if z=59 when x=8 and y=8, find Z if x=3 and y=4
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!