In the above figure (not drawn to scale), Find ∠AEC.
2 answers:
Answer:
C. 75°
Step-by-step explanation:
We have been given a circle and we are asked to find the measure of angle AEC.
We will use Intersecting chords theorem to find the measure of angle AEC, which states that measure of angle formed inside a circle by two intersecting chords is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.
We can see that measure of arc AC is 110 degrees and measure of its vertical arc BD is 40 degrees.
Therefore, measure of angle AEC is 75 degrees and option C is the correct choice.
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Answer:
1) View image attached
2) -3, -2.5, -1, 2, 5
3) -2.5
Step-by-step explanation:
1) Draw a number line, an image is shown below with the number line. You then put "points" on the values that you are plotting. This is also shown in the image attached.
2) The ones with the "-" are negative, meaning that they are below 0. These will always be smaller than those without a "-" sign. In addition to this, the way negative numbers work in terms of least to greatest is completely flipped. For example, -5 is greater than -10, and -10 is less than -5. If the numbers were positive, 5 would be less than 10 and 10 would be greater than 5.
3) The value that isn't an integer is the one that isn't a whole number. In those answer choices you gave, the only one with a decimal is -2.5 (as indicated by the ".5"
Answer:
41°
Step-by-step explanation:
This problem involving the Law of Cosines has been mostly worked for you. The value of the cosine is the solution to the remaining one-step linear equation. The inverse cosine function (cos⁻¹ or arccos) is used to find the angle from the value of the cosine.
-1125 = -1500·cos(A)
cos(A) = -1125/-1500 = 3/4 . . . . . divide by -1500 (this is the one step)
A = arccos(3/4) ≈ 41.4096°
The angle formed by the lines to the lampposts is about 41°.
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<em>Additional comment</em>
If you find the angle using the ACOS( ) function of a spreadsheet, you will always get the result in radians. Most calculators offer the choice of units for angles, so be sure you set the mode appropriately.
In the calculator screenshot, there is a decimal point in the fraction to force the angle result to be displayed as a numerical value. Otherwise, this calculator shows cos⁻¹(3/4), which isn't terribly helpful.
