How do you construct a scalene triangle ABC where m<A=45 degrees and m<B=30 degrees?

A scalene triangle is a triangle that has three unequal sides.

The question is asking you to draw a scalene triangle. Label its vertices (where its sides meet) A, B, and C. Then, mark angle A 45 degrees and angle B 30 degrees. You can also label angle C using the property that all triangles have angles that add up to 180 degrees.

Construction:

Make a perpendicular bisector (90 deg). Bisect that angle to get 45.

Now you have one angle. For the 30 deg angle, set your compass to some arbitrary length. measure up the perpendiculare bisector that arbitrary length, mark that arc, and measure from that arc up the length again. Set you compass now for that double distance, and measuring from the first arc (the first arc mark), cast an arc across the base line . You have constructed a 30 degree angle (side opposite 1/2 of the hypotenuse).
connect the 45 degree line to the line coming from the vertex of the 30 degree angle, and you have it.

To construct a scalene triangle ABC with angle A measuring 45 degrees and angle B measuring 30 degrees, you can follow these steps:

1. Start by drawing a straight line segment, which will serve as the base of your triangle. Let's call this line segment AB.

2. At point A, draw a ray to form an angle of 45 degrees. To draw a 45-degree angle, you can use a protractor or follow this method:
- Set your compass to any convenient radius and place the compass on point A.
- Draw an arc that intersects line segment AB on both sides. Label the points of intersection as C and D.
- Draw a line connecting A and C. This line will be at a 45-degree angle to line segment AB.

3. From point B, draw another ray to form an angle of 30 degrees. You can use the same method as in step 2 but adjust the angle to 30 degrees.

4. Where the two lines from steps 2 and 3 intersect, label this point C. This will be the third vertex of your triangle.

5. Connect points A and C, as well as points B and C, to form the sides of the triangle.

Now, you have constructed a scalene triangle ABC, where angle A measures 45 degrees and angle B measures 30 degrees.