non-right-angled trigonometry

Question 1

what does the mnemonic ‘SOH CAH TOA’ stand for?

Answer 1

sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent

Question 2

what is an angle of elevation?

Answer 2

an angle of elevation is an angle measured upwards from the horizontal

Question 3

what is an angle of depression?

Answer 3

an angle of depression is an angle measured downwards from the horizontal

Question 4

what is a compass bearing?

Answer 4

a compass bearing is a direction given by stating the angle either side of north or south, such as S60ºE

Question 5

what is a true bearing?

Answer 5

a true bearing is a direction given by measuring the angle clockwise from the north to the required direction, such as 120ºT

Question 6

how do you find an obtuse angle, as opposed to an acute angle?

Answer 6

180 - (acute angle)

Question 7

what is the formula to find the area of a triangle?

Answer 7

A = 1 absinC
—
2

where A - area
a - side a
b - side b
C - angle C

Question 8

what is the sine rule?

Answer 8

a = b = c
—– —– —–
sinA = sinB = sinC

sin A = sinB = sinC
—– —– —–
a = b = c

where a - side a
b - side b
c - side c
A - angle A
B - angle B
C - angle C

Question 9

what is the cosine rule?

Answer 9

to find the third side of a triangle:
c² = a² + b² - 2abcosC

to find an angle given three sides of a triangle:
cosC = a² + b² - c²
————–
2ab

where c - side c
a - side a
b - side b
C - angle c

Question 10

what is a radial survey?

Answer 10

a radial survey is used to create a diagram of a piece of land that is in the shape of a polygon. it involves drawing lines from a central point radiating out to the corners of the polygon. the length of the lines and the angles between them at the central point (usually labelled O for ‘origin’) are measured