How to construct a Triangle ABC in which BC=4.8cm, Angle B=60° and Angle C=75°.
You draw segment BC first.
Then you use the protractor and mark 60 so you draw line at 60
the same for 75 ,and you connect the lines.
BC=4.8cm,angle B=60°,angle C=75°
To construct triangle ABC given BC=4.8cm, Angle B=60°, and Angle C=75°, you can follow these steps:
Step 1: Draw a line segment BC of length 4.8cm.
Step 2: At point B, use a protractor to measure an angle of 60°. Mark the endpoint as A.
Step 3: At point C, use a protractor to measure an angle of 75°. Mark the endpoint as A.
Step 4: Now, draw a line segment AC connecting points A and C.
Step 5: Triangle ABC is now constructed.
To find the length of side AB, you can use the law of sines, which states that in any triangle:
a/sin(A) = b/sin(B) = c/sin(C),
where a, b, and c represent the lengths of the sides, and A, B, and C represent the opposite angles, respectively.
Since we have Angle B and Angle C, we can use the law of sines to find the length of side AB.
Step 1: Substitute the given values into the formula:
AB/sin(60°) = 4.8cm/sin(75°).
Step 2: Rearrange the formula to solve for AB:
AB = (4.8cm * sin(60°)) / sin(75°).
Step 3: Use a calculator to find the value of AB:
AB ≈ 4.19cm.
Therefore, the length of side AB is approximately 4.19cm.