Answer:
EH = 3.31
Step-by-step explanation:
We have been given a right angle triangle EKL. As KH has been given as the altitude (perpendicular) of the right angled triangle, and K is the right angle, we can say that EK is tthe base of the triangle and EH is the only side lleft, which is the hypotenuse of the triangle.
Where,
EK = Base = 3
KH = perpendicular altitude
EH = Hypotenuse
m<K = 90
m<E = 25
We know that
cosθ = Base/ Hypotenuse
cos 25 = 3/ EH
EH = 3/cos25
EH = 3.31
Perpendicular alitutude can also be calculated by using the formula for tanθ.
Answer:
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Step-by-step explanation
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
The distance Terry needs to run when the winner crosses the finish line is 1. 6 miles.
<h3>How to find the distance Terry needs to run?</h3>
The race was a 10 km race and she has completed 74% of the race when the winner crosses the finish line.
Therefore, the number of more miles Terry need to cover can be calculated as follows:
74 / 100 × 10 = 740 / 100 = 7.4 km
He has covered 7.4 km.
The distance remaining to cover = 10 km - 7.4 km = 2.6 km
Therefore,
4km = 2.48 miles
2.6 km = ?
cross multiply
The distance remaining to cover(miles) = 2.6 × 2.48 / 4
The distance remaining to cover(miles) = 6.448 / 4
The distance remaining to cover(miles) = 1.612
The distance remaining to cover(miles) = 1.6 miles
learn more on distance here:brainly.com/question/13471766
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