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2 years ago

Please help on math hw will mark brainliest

Mathematics

1 answer:

erma4kov [3.2K]2 years ago

4 0

Answer:

∠ACB 107°

Step-by-step explanation:

1.) First, by using straight angle theorem we can determine that ∠CED is equal to 180 - 147 which is 33°.

2.) Next, using alternate interior angles theorem we know that ∠CDE = ∠ABC which is 40°

3.) Then, because of the angle sum theorem we know that all the angles of the triangle must add to 180° and we can therefore solve for ∠DCE using the equation 33 + 40 + x = 180 where x is ∠DCE. By solving this we get 107°.

4.) Finally, using vertical angles theorem we know that ∠DCE = ∠ACB and so ∠ACB is 107°

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The bearing of Q from P is 150

Lynna [10]

Answer:

(i) see first attached diagram

(ii) QR = 22.67 km (2 dp)

(iii) 243°

Step-by-step explanation:

A bearing is the angle in degrees measured clockwise from north.

Part (i)

see first attached diagram

Part (ii)

The angles marked in blue on the second attached diagram are Consecutive Interior Angles. In this case they add to 180° as the North lines are parallel.

The sum of angles around a point is 360°

⇒ m∠QPR (shown in red on the second attached diagram) = 360 - 150 - (180 - 15) = 45°

To calculate the distance between Q and R (marked in red on the attached diagram), use the cosine rule.

⇒ QR² = PR² + QP² - 2(PR)(QP)cos(QPR)

⇒ QR² = 32² + 24² - 2(32)(24)cos(45)

⇒ QR² = 513.8839841...

⇒ QR = √513.8839841...

⇒ QR = 22.67 km (2 dp)

Part (iii)

We need to find the angle marked in green on the third attached diagram.

To do this, we need to find the angle marked in pink and the angle marked in orange, then subtract them from 360°

Pink angle = 180 - 150 = 30° (using the same consecutive angle theorem as before)

Orange angle (o) using the sine rule:

⇒ sin(o)/32 = sin(45)/QR

⇒ sin(o) = 32sin(45)/22.67

⇒ sin(o) = 0.9981652337...

⇒ o = 86.52868176...°

Therefore, the green angle = 360 - 30 - 86.52868176... = 243° (nearest degree)

8 0

2 years ago

Plz help pe with this guys, thank you.

Burka [1]

31.+ addition
32. - subtraction

7 0

3 years ago

Find the exact value of the trigonometric expression given that sin u = − 8 17 and cos v = − 24 25 . (Both u and v are in Quadra

Rashid [163]

Answer: sin u = -5/13 and cos v = -15/17

Step-by-step explanation:

The nice thing about trig, a little information goes a long way. That’s because there is a lot of geometry and structure in the subject. If I have sin u = opp/hyp, then I know opp is the opposite side from u, and the hypotenuse is hyp, and the adjacent side must fit the Pythagorean equation opp^2 + adj^2 = hyp^2.

So for u: (-5)^2 + adj^2 = 13^2, so with what you gave us (Quad 3),

==> adj of u = -12 therefore cos u = -12/13

Same argument for v: adj = -15,

opp^2 + (-15)^2 = 17^2 ==> opp = -8 therefore sin v = -8/17

The cosine rule for cos (u + v) = (cos u)(cos v) - (sin u)(sin v) and now we substitute: cos (u + v) = (-12/13)(-15/17) - (-5/13)(-8/17)

I am too lazy to do the remaining arithmetic, but I think we have created a way to approach all of the similar problems.

3 0

2 years ago

Simplify the expression

raketka [301]

Answer:

147

Step-by-step explanation:

82+9(12÷3×2)-7

82+9(4×2)-7

82+9(8)-7

82+72-7

154-7

147

Follow PEMDAS

3 0

2 years ago

This is not a question

BlackZzzverrR [31]

Why did you post it if it’s not a question lol

7 0

3 years ago