Use any tools to construct each of the following, if possible:
a. A right triangle with one acute angle measuring 75° and a leg of 5 cm on a side of the 75° angle
b. A triangle with angles measuring 30°, 60°, and 90°
constrct a triangle LMN in which MN=9cm angle M=30 degree and angle N=75 degree.Draw a median through L and measure its length.
To construct the triangles described, you can use various tools such as a ruler, compass, and protractor. Here's how you can construct each triangle:
a. Right Triangle with a 75° acute angle and a 5 cm leg:
1. Start by drawing a line segment of any length to act as the hypotenuse of the triangle.
2. Using a protractor, construct a 75° angle at one of the endpoints of the line segment. This angle will be one of the acute angles of the right triangle.
3. Using a ruler, measure and mark a 5 cm line segment along the ray of the 75° angle, starting from the angle vertex.
4. Connect the endpoint of the 5 cm line segment to the original endpoint of the hypotenuse line segment. This line will be the other leg of the right triangle.
5. Finally, erase any unnecessary construction lines and label the sides of the triangle accordingly.
b. Triangle with angles measuring 30°, 60°, and 90°:
1. Begin by drawing a line segment of any length to act as the base of the triangle.
2. Using a protractor, construct a 30° angle from one endpoint of the base line segment. This angle will be the smallest angle in the triangle.
3. From the same endpoint of the base, use a protractor to construct a 60° angle in the opposite direction. This angle will be the second largest angle in the triangle.
4. Connect the other endpoints of the two constructed angles with a straight line. This line will form the remaining side of the triangle and will be perpendicular to the base.
5. Finally, erase any unnecessary construction lines and label the sides and angles accordingly.