Answer:
050
115
223
Step-by-step explanation:
bearings are a measurement in degrees from North
so from point A draw a North line , then draw a line to B ( the position) the angle is the bearing.
as a full turn would be a circle 360⁰ , bearings are written as 3 digits
Remember that : aⁿ.aˣ = aⁿ⁺ˣ ( Example 5³.5⁶ = 5³⁺⁶ = 5⁹)
Apply the same logic for:
5⁴/₃ x 5⁸/₃
Add up the exponents: 4/3 + 8/3 = 12/3 = 4, then
5⁴/₃ x 5⁸/₃ = 5⁴
Answer:
√5.
Step-by-step explanation:
Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse = √(1^2 + 2^2) = √5 (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).
so cos A = adjacent / hypotenuse = 2/√5.
and sin A = opposite / hypotenuse = 1 / √5
cos A / sin A = 2/√5 / 1/ √5 = 2.
sin A / (1 + cos A) = 1/√5 (1 + 2/ √5)
= 1 / √5 ( (√5 + 2) /√5)
= 1 / (√5 + 2)
So the answer is:
2 + 1 /(√5 + 2).
We can simplify it further by multiplying top and bottom of the fraction by the complement of √5 + 2 which is √5 - 2.
2 + 1 / (√5 + 2)
= 2(√5 + 2) + 1 / (√5 + 2 )
= { 2(√5 + 2) + 1 } / (√5 + 2)
Multiplying this by √5 - 2 / √5 - 2 we get:
(2(5 - 4) + √5 - 2) / (5 -4)
= 2 + √5 - 2 / 1
= √5.
In a dollar amount, it would round to 50 cents.
