Chris is standing due south of a 20m flagpole at a point where the angle of elevation of the top of the pole is 35. Brandyn is s
tanding due east of the flagpole at a point where the angle of elevation of the top of the pole is 27. How far is Brandyn from Chris?
1 answer:
Answer:
Brandyn is 41.48m from Chris
Step-by-step explanation:
I have drawn an image depicting this question and I've attached it.
From the diagram, chris is standing at point B while Brandyn is at point D. x is the distance of brandyn to the bottom of the pole.
The height of the pole is AC.
Now, by trigonometric ratio, we can find AC. Thus;
AC/20 = tan 35
AC = 20 tan 35
AC = 14
Since,we now have AC, we can find x.
Similarly, 14/x = tan 27
x = 14 / tan 27
x = 27.48 m
Thus, total distance of brandyn from Chris = 14 + 27.48 = 41.48 m
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As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.
Angles <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>
Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles.
BAQ = QRP because they are alternate interior angles.
Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.
As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.
Angles <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>
Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles.
BAQ = QRP because they are alternate interior angles.
Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.