1. Triangle ABC has a 63.0-degree angle at B, and side AC is 13.6 cm long. What is the diameter of the circle circumscribed about ABC?
2. And: Given any triangle ABC, with sides a, b, and c opposite angles A, B,
and C, respectively, what can be said about the three ratios a/sinA , b/sinB
, and c/sinC ? This result is known as the Law of Sines.
in triangle ABC,m<A=80 degrees and AB> AC. what is the smallest angle
1. To find the diameter of the circle circumscribed about triangle ABC, you can use the property that the circumcenter of a triangle is the intersection point of the perpendicular bisectors of its sides.
To solve this problem, you can follow these steps:
Step 1: Draw triangle ABC and label the given information. Angle B is given as 63.0 degrees, and side AC is given as 13.6 cm.
Step 2: Construct the perpendicular bisectors of sides AB and BC. To do this, draw lines perpendicular to AB and BC at their midpoint. Let's call the intersection point of these bisectors point O.
Step 3: Measure the distance from point O to any vertex of the triangle. This distance is the radius of the circumcircle. You can use a ruler or compass to measure it accurately.
Step 4: Multiply the measured radius by 2 to get the diameter of the circle. This will give you the answer to the question.
2. The Law of Sines relates the ratios of the lengths of the sides of a triangle to the sines of their opposite angles. It states that in any triangle ABC,
a/sinA = b/sinB = c/sinC
This law is useful for solving various problems involving triangles, especially when you have information about the angles and sides but not enough to use other methods, such as the Law of Cosines.
To apply the Law of Sines, follow these steps:
Step 1: Identify the given information in the triangle. You need to know at least one side length and its corresponding opposite angle.
Step 2: Choose a ratio from the Law of Sines equation. For example, if you have side a and angle A, you can use the ratio a/sinA.
Step 3: Substitute the known values into the chosen ratio and solve for the unknown.
Step 4: Repeat the process using the other ratios to find other unknowns, if applicable.
Note: The Law of Sines holds true for all triangles, whether they are acute, obtuse, or right triangles. However, it may not yield a unique solution in some cases, such as when given an angle-side-side combination. Additionally, for some triangles, the Law of Sines may only provide an estimate or not be applicable at all.