The point (-9, 40) is on the terminal arm of an angle, $\theta$θ in standard position.
a. what is the length of the line segment connecting the orgin to the point (-9,40)
b. Determine the measure of $\theta$θ , to the nearest tenth of a degree.
6 years ago
Answered By Chris W
I made a right angle triangle with the coordinate of the point. The accidentally curvy black line is the hyportenuse, which is also the length of the line segment connecting the origin to this point.
So we can find this length with Pythagorean theory
(-9)2 + (40)2 = c2
81 + 1600 = c2
1681 = c2 (now squareroot both sides)
41 = c
Find the angle we can use the tangent function (tan x = opposite over adjacent). And first let's just use positive values and adjust for the quadrant after.
tan x = 40/9
x = tan-1 (40/9)
x = 77.32 degrees
Now let's find that angle in quadrant II
180 - 77.32 = 102.7 degrees (tp the nearest tenth)
6 years ago
Answered By Chris W
I made a right angle triangle with the coordinate of the point. The accidentally curvy black line is the hyportenuse, which is also the length of the line segment connecting the origin to this point.
So we can find this length with Pythagorean theory
(-9)2 + (40)2 = c2
81 + 1600 = c2
1681 = c2 (now squareroot both sides)
41 = c
Find the angle we can use the tangent function (tan x = opposite over adjacent). And first let's just use positive values and adjust for the quadrant after.
tan x = 40/9
x = tan-1 (40/9)
x = 77.32 degrees
Now let's find that angle in quadrant II
180 - 77.32 = 102.7 degrees (tp the nearest tenth)
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