Answer:
A. 180
Step-by-step explanation:
The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of
the circle circumscribed about this triangle.
Answer in CM, please. Thanks!
Answer in CM, please. Thanks!
1 answer:
Answer:
16cm
Step-by-step explanation:
To find the diameter we must first find the radius and multiply by 2.
The isosceles triangle that has the length of a leg to be 8cm and a vertex angle of that has been circumscribed is shown in the attachment.
We draw a line from the vertex of the isosceles triangle that bisects the base through the center O of the circle.
This implies that .
Based on this because the two radii are equal.
It follows that: because sum of angles in a triangle must be 180 degrees.
This means that, triangle AOC is an equilateral triangle, hence all sides are equal.
One side of this equilateral triangle happens to be the side of the leg of the isosceles triangle which is 8cm.
It follows that, the radius of the circle is 8cm.
Therefore the diameter of the circle is 16cm
You might be interested in
Answer:
The correct option: (2) Triangle ABC that has angle measures 45°, 45° and 90°.
Step-by-step explanation:
It is provided that a triangle ABC has an acute angle for which the sine and cosine ratios are equal to 1.
Let the acute angle be m∠A.
For the sine and cosine ratio of m∠A to be equal to 1, the value of Sine of m∠A should be same as value of Cosine of m∠A.
The above predicament is possible for only one acute angle, i.e. 45°, since the value of Sin 45° and Cos 45° is,
So for acute angle 45° the ratio of Sin 45° and Cos 45° is:
Hence one of the angles of a triangle is, m∠A = 45°.
Comparing with the options provided the triangle is,
Triangle ABC that has angle measures 45°, 45° and 90°.
Thus, the provided triangle is a right angled isosceles triangle, since it has two similar angles.
