Question

Construct triangle ABC, in which AB=5cm , angle BAC=95° and angle ABC=34°. Measure the length of BC.

Answer 1

To construct triangle ABC with AB=5cm, angle BAC=95°, and angle ABC=34°, draw line segment AB and measure the angles. Then, draw line segment BC and calculate its length using the Sine Rule.

Step-by-step explanation:

To construct triangle ABC, we start by drawing a line segment AB with a length of 5cm. Then, using a protractor, we measure an angle of 95° at point A and an angle of 34° at point B.

Next, we draw a line segment BC from point B, making sure it intersects with line segment AB. The length of BC can be determined using the Sine Rule or the Cosine Rule.

By using the Sine Rule, we can calculate BC as follows:

1. Calculate angle ACB = 180° - angle BAC - angle ABC
2. Use the Sine Rule: BC / sin(angle ABC) = AB / sin(angle ACB)
3. Substitute the given values: BC / sin(34°) = 5cm / sin(51°)
4. Solve for BC: BC = sin(34°) * (5cm / sin(51°))

After evaluating the expression, we find that the length of BC is approximately 3.59cm.