CONSTRUCT TRIANGLEABC AB=7CM ,AC=9.5 AND B=120 MEASURE BC
To construct triangle ABC, we will need to follow these steps:
Step 1: Draw a line segment AB of length 7 cm.
Step 2: At point A, draw a ray AC making an angle of 120 degrees with AB.
Step 3: With A as the center and a radius of 9.5 cm, draw an arc that intersects AC. Let the point of intersection be labeled as B.
Step 4: Connect points B and C to form triangle ABC.
Now that we have constructed triangle ABC, we need to find the measure of BC. To find the length of BC, we can use the Law of Cosines, which states:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this equation, a, b, and c refer to the lengths of the sides of the triangle ABC, and C refers to the angle opposite side c (in this case, angle B).
To use the Law of Cosines, we have:
c^2 = 7^2 + 9.5^2 - 2 * 7 * 9.5 * cos(120)
Now, we can calculate the value of BC as follows:
c^2 = 49 + 90.25 - 133 * (-0.5)
c^2 = 49 + 90.25 + 66.5
c^2 = 205.75
To find the length of BC, we take the square root of both sides:
c = sqrt(205.75)
c ≈ 14.34 cm
Therefore, the approximate length of BC in triangle ABC is 14.34 cm.
so, did you construct the triangle?
if so, measure BC.
Or, just use the law of sines to find C, then you know A, and you can use either law of sines or cosines to find BC
what did you get?