Construct triangle XYZ such that angle x=60° angle z=45° and xz=8cm measure xy
I assume you can construct the two angles
(google them if not)
then draw XZ of length 8,
construct angles X and Z
where their rays intersect is Y
Draw it
angle y = 180 - 45 -60 = 75
law of sines
(sin 75 ) / 8 = (sin 45) / xy
To construct triangle XYZ with the given conditions, follow these steps:
Step 1: Draw a straight line segment XY of any length (e.g., 10 cm).
Step 2: At point X, use a protractor to measure an angle of 60°. Mark a point where the angle intersects the line XY and label it as Z.
Step 3: From point Z, draw a line segment ZX of 8 cm in length to create side XZ.
Step 4: Using a protractor, measure an angle of 45° at point Z. Label the point where the angle intersects the line ZX as Y.
Step 5: Finally, draw a line segment YX to complete the triangle XYZ.
Your triangle XYZ is now constructed with angle X = 60°, angle Z = 45°, side XZ = 8 cm, and side XY depending on the length you initially drew.
To construct triangle XYZ, you need to follow a series of steps:
Step 1: Draw a base line XY. This will be the side opposite to angle Z.
Step 2: From point X, use a protractor to measure and mark angle X with 60 degrees.
Step 3: From point Z, use a protractor to measure and mark angle Z with 45 degrees.
Step 4: Draw a line segment XZ, starting from angle X and ending at angle Z, by using a ruler.
Step 5: Measure and mark line segment XZ as 8 cm.
Step 6: From point Y, draw a line that intersects line segment XZ at a right angle. This will form the perpendicular bisector of line segment XZ.
Step 7: Mark the point of intersection between the perpendicular bisector and line segment XZ as point O.
Step 8: Draw line segments OY and OX, connecting point O to points X and Y, respectively.
Now, triangle XYZ is constructed such that angle X is 60 degrees, angle Z is 45 degrees, and the length of XY can be measured using a ruler.