Consider the attached figure. If AB has length 1, then BC has length sin(15°) and CD (the altitude of triangle ABC) has length sin(15°)·cos(15°).
By the double angle formula for sin(α), ...
... sin(2α) = 2sin(α)cos(α)
Rearranging, this gives
... sin(α)·cos(α) = sin(2α)/2
We have
... CD = sin(15°)·cos(15°) = sin(2·15°)/2
... CD = sin(30°)/2 = (1/2)/2 = 1/4
That is, the altitude, CD, is 1/4 the hypotenuse, AB, of triangle ABC.
Answer:
Part A - D:8
Part B - C:140°
<h3>Solving/Reasoning:</h3>
Part A: Vertical angles are always congruent.
Part B: If angles are supplementary, they need to equal 180 when added together. Since we know angle A is 40, we can subtract it from 180 and figure out what is left over that should be angle B.
40+B=180
B=180-40
B=140
The number of edges of a polyhedron with 4 faces and 4 vertices will be 6.
<h3>What is a polygon?</h3>
The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
Using Euler's formula, the number of the edges does a polyhedron with 4 faces and 4 vertices have
We know the formula for the edges of the polyhedron will be
F + V = E + 2
The number of faces, vertices, and edges of a polyhedron are denoted by the letters F, V, and E.
Then we have
4 + 4 = E + 2
E = 8 - 2
E = 6
More about the polygon link is given below.
brainly.com/question/17756657
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Step-by-step explanation:
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