Draw a trianglw whose perimeter is 13.3 cm and base angles are 45 degree and 60 degree
the angles are ... 45º , 60º , 75º
the sides are in the same ratio as the sines of the angles
k[sin(45º) + sin(60º) + sin(75º)] = 13.3 cm
solve for k (the constant of proportionality)
... k times the sine of an angle gives the length of the opposite side
In google type:
Construction of a Triangle of a given Perimeter and Base Angles
When you see list of results click on:
gradestack.c o m
You wil see construction method.
To draw a triangle with a perimeter of 13.3 cm and base angles of 45 degrees and 60 degrees, we can follow these steps:
Step 1: Start by drawing a base for the triangle. Since the base angles are 45 degrees and 60 degrees, we can draw a line segment as the base.
Step 2: Measure the length of the base line segment. This length will be one side of the triangle.
Step 3: Divide the remaining perimeter (13.3 - length of the base) into two equal parts. These two parts will represent the remaining two sides of the triangle.
Step 4: To find the length of the remaining two sides, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. In this case, we have two sides and their opposite angles (45 and 60 degrees) known.
a/sin(A) = b/sin(B) = c/sin(C)
Let's assume the length of the base is 'a', the length of the side opposite to the 45-degree angle is 'b', and the length of the side opposite to the 60-degree angle is 'c'. Then we have the following equations:
a/sin(45) = b/sin(60) = c/sin(180 - 45 - 60)
Solving these equations will give us the lengths of the remaining two sides.
Step 5: Using the lengths of the three sides obtained, draw the remaining sides of the triangle to complete the shape.
Remember to use a protractor and ruler accurately while drawing the angles and lengths to ensure the triangle is constructed correctly.