A skier moves 100.0 m horizontally, and then travels another 35.0 m uphill at an angle of 35.0º above the horizontal. What is th
e skier's displacement from his starting point? (Use the graphical method to answer and include your scale on the graph paper.) Give both the magnitude and the angle in your answer.
1 answer:
Because there isnt 90 degrees angle in this triangle (triangle - starting point - point where he starts climbing- ending point) we will use cosine law to find magnitude of displacement. For cosine law we need 2 sides of triangle and angle between them which is exactly what is given.
a^2 = b^2 + c^2 - 2*b*c*cos(alpha)
after expressing values we get:
a^2 = 10000 + 1225 + 5734
a = 130,2 meters
to calculate angle we again use cosine law but now our unknown variable is angle alpha. our sides we will use are 100 meters and 130,2 meters because we need angle between them.
cos(alpha) = (b^2 + c^2 - a^2)/(2*b*c)
cos(alpha) = 0.98
alpha = 8.89 degrees
a^2 = b^2 + c^2 - 2*b*c*cos(alpha)
after expressing values we get:
a^2 = 10000 + 1225 + 5734
a = 130,2 meters
to calculate angle we again use cosine law but now our unknown variable is angle alpha. our sides we will use are 100 meters and 130,2 meters because we need angle between them.
cos(alpha) = (b^2 + c^2 - a^2)/(2*b*c)
cos(alpha) = 0.98
alpha = 8.89 degrees
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Answer:
Step-by-step explanation:
x = measure of the first angle
y = measure of the second angle
z = measure of the third angle
The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)
The third angle is 14 more than the second
And remember that the sum of these three angles must be equal to 180.
Let's take these equations
If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....
Distribute the + sign
Combine like terms;
Divide by 6.
We have now defined that the measure of the first angle is 30º.
Let's take another equation... for example
I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.
Distribute the + sign and Combine like terms;
Subtract 44 to isolate 2y.
Now divide by 2.
We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.
Answer:
20.
Step-by-step explanation:
This can be solved using combination technique. Since we have to choose 3 out of 6 and their order is not considered. Thus,
6 combination 3
= 6C3
=
=
=
=
= 5*4
= 20 ANSWER