Given the diagram below. If G is the circumcenter of ABC. DC = 16, GB = 21 and AZ = 19, find each measure.
1 answer:
Answer:
Step-by-step explanation:
Properties of a circumcenter;
1). Circumcenter of a triangle is a point which is equidistant from all vertices.
2). Point where perpendicular bisectors of the sides of a triangle meet is called circumcenter of the triangle.
From the picture attached,
9). AG = GB = GC = 21
10). BC = 2(DC)
= 2×16
= 32
11). By applying Pythagoras Theorem in ΔGFB,
GB² = GF² + FB²
(21)² = GF² + (19)²
441 = GF² + 361
GF² = 441 - 361
GF =
GF = 8.9
12). By applying Pythagoras theorem in ΔGDB,
GB² = DG² + BD²
(21)² = (DG)² + (16)² [BD = DC = 16]
DG² = 441 - 256
DG = √185
DG = 13.6
You might be interested in
Answer:
The three questions about the given triangle has been answered below.
Step-by-step explanation:
We are given a right angled triangle whose sides are of length 20, 21 and 29.
<u>(1)</u> sin(B) =
=
= 0.72
<u>(2)</u> sin(A) =
sin(A) = 0.689
∠CAB =
∠CAB = 43.551°
<u>(3)</u> We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.
From the given options the angles that satisfy this are 55 , 66 and 75.
45 is not included as then sinA = cosA and that condition is not there.
Answer:
<h2>The answer is 13.4 units</h2>Step-by-step explanation:
The distance between two points can be found by using the formula
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
A (10,-1) and B (-2,5)
The distance is
We have the final answer as
<h3>13.4 units to the nearest tenth</h3>Hope this helps you