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2 years ago

Find the values for θ that make each statement true. a. sinθ=cos32 b. cosθ=sin(θ+20).

Mathematics

1 answer:

faltersainse [42]2 years ago

8 0

Answer:

a. 58

b. 35

Step-by-step explanation:

a. Given,

sinθ = cos 32

We know that cos x = sin (90 - x)

⇒ sin θ = sin (90 - 32)

⇒ sin θ = sin 58

⇒ θ = 58

Thus, the value of θ would be 58.

b. Given,

cosθ = sin(θ+20),

sin (90 - θ) = sin (θ + 20)

⇒ 90 - θ = θ + 20

⇒ 90 - 20 = θ + θ

⇒ 70 = 2θ

⇒ θ = 35

Thus, the value of θ would be 35.

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The radius of a semicircle is 4 miles. What is the semicircle's area?

adell [148]

Answer:

8 $\pi$ miles or 25.133 miles

Step-by-step explanation:

your radius is 4 miles.

The area of a circle is A= $\pi r^{2}$

Therefore, the area of this circle is $4^{2} \pi$ , or 16 $\pi$

Half of this area, because what you're looking for is a semi-circle, is:

8 $\pi$ (exact) or 25.133 (rounded) miles.

6 0

2 years ago

A ship leaves port at 10 miles per hour, with a heading of N 35° W. There is a warning buoy located 5 miles directly north of th

Leno4ka [110]

The value of the angle subtended by the distance of the buoy from the

port is given by sine and cosine rule.

The bearing of the buoy from the is approximately 307.35°

Reasons:

Location from which the ship sails = Port

The speed of the ship = 10 mph

Direction of the ship = N35°W

Location of the warning buoy = 5 miles north of the port

Required: The bearing of the warning buoy from the ship after 7.5 hours.

Solution:

The distance travelled by the ship = 7.5 hours × 10 mph = 75 miles

By cosine rule, we have;

a² = b² + c² - 2·b·c·cos(A)

Where;

a = The distance between the ship and the buoy

b = The distance between the ship and the port = 75 miles

c = The distance between the buoy and the port = 5 miles

Angle ∠A = The angle between the ship and the buoy = The bearing of the ship = 35°

Which gives;

a = √(75² + 5² - 2 × 75 × 5 × cos(35°))

By sine rule, we have;

$\displaystyle \frac{a}{sin(A)} = \mathbf{ \frac{b}{sin(B)}}$

Therefore;

$\displaystyle sin(B)= \frac{b \cdot sin(A)}{a}$

Which gives;

$\displaystyle sin(B) = \mathbf{\frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }}$

$\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx 37.32^{\circ}$

Similarly, we can get;

$\displaystyle B = arcsin\left( \frac{75 \cdot sin(35^{\circ})}{\sqrt{75^2 + 5^2 - 2 \times 75\times5\times cos(35^{\circ}) } }\right) \approx \mathbf{ 142.68^{\circ}}$

The angle subtended by the distance of the buoy from the port, C is therefore;

C ≈ 180° - 142.68° - 35° ≈ 2.32°

By alternate interior angles, we have;

The bearing of the warning buoy as seen from the ship is therefore;

Bearing of buoy ≈ 270° + 35° + 2.32° ≈ 307.35°

Learn more about bearing in mathematics here:

brainly.com/question/23427938

5 0

2 years ago

Solve for n. n+ 1 = 4(n-8) On=1 O n= 8 on = 11 On = 16

Lesechka [4]

Answer:

n = 11

Step-by-step explanation:

n+ 1 = 4(n-8)

<=> n + 1 = 4n - 4×8

<=> 4n - n = 1 + 4×8

<=> 3n = 33

<=> n = 11

3 0

2 years ago

Bill will randomly pick one marker a bag and one crayon from another bag.There are three red markers, 2 green markers , and 1 bl

Tanzania [10]

Answer:

i believe it is 2/6

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

8/x = 32 ..................

krok68 [10]

Answer:

Step-by-step explanation:

x= 1/4

6 0

2 years ago