Write 1 and 1/3 as an improper fraction
2 answers:
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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.
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<u>Part (i)</u>
see first attached diagram
<u>Part (ii)</u>
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)
<u>Part (iii)</u>
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)
The missing number is 20.
<h3>What is the missing number?</h3>Subtraction is the mathematical operation that is used to find the difference between two or more numbers.
In order to find the missing number, subtract the total number of people who like science and mathematics from the total number of people who like science
38 - 18 = 20
To learn more about subtraction, please check: brainly.com/question/854115
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