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Construct triangle ABC with side AB = 7cm, angle BAC = 50 degrees, and angle ABC = 70 degrees.

Mathematics

ScanSolve AI Answer

Step-by-step solution

4 steps

Okay Mallam, let's construct triangle ABC with the given measurements.

Here are the steps to construct triangle ABC, indicating where to stand and draw marks (which act like arcs for angle measurement):

  1. Draw the base line segment AB.

    • Draw a straight line using a ruler.
    • Stand your pencil or compass point at a starting point on the line and label it A.
    • Using your ruler, measure 7 cm7 \text{ cm} from point A along the line. Stand your pencil or compass point at this 7 cm7 \text{ cm} mark and label it B.
    • Draw a clear line segment connecting A and B.
  2. Construct ∠BAC=50∘\angle BAC = 50^\circ at point A.

    • Place the center of your protractor exactly on point A.
    • Align the baseline of the protractor with the line segment AB.
    • Starting from 0∘0^\circ on the scale that aligns with AB, count up to 50∘50^\circ.
    • Make a small mark (this is your "specific arc" for the angle) on your paper at the 50∘50^\circ reading.
    • Draw a long ray (a line extending outwards) from point A passing through this mark.
  3. Construct ∠ABC=70∘\angle ABC = 70^\circ at point B.

    • Place the center of your protractor exactly on point B.
    • Align the baseline of the protractor with the line segment BA (make sure the 0∘0^\circ mark is on the side of A).
    • Starting from 0∘0^\circ on the scale that aligns with BA, count up to 70∘70^\circ.
    • Make a small mark (your "specific arc" for this angle) on your paper at the 70∘70^\circ reading.
    • Draw a long ray from point B passing through this mark.
  4. Locate point C and complete the triangle.

    • The point where the ray from A and the ray from B intersect is point C.
    • You have now constructed triangle ABC.

    Regarding part (c) from your image:
    The question asks "What type of triangle is triangle ABC?".
    Given ∠BAC=50∘\angle BAC = 50^\circ and ∠ABC=70∘\angle ABC = 70^\circ, the third angle ∠ACB\angle ACB would be:

    ∠ACB=180∘−(∠BAC+∠ABC)\angle ACB = 180^\circ - (\angle BAC + \angle ABC) ∠ACB=180∘−(50∘+70∘)\angle ACB = 180^\circ - (50^\circ + 70^\circ) ∠ACB=180∘−120∘\angle ACB = 180^\circ - 120^\circ ∠ACB=60∘\angle ACB = 60^\circ

    Since all three angles (50∘,70∘,60∘50^\circ, 70^\circ, 60^\circ) are less than 90∘90^\circ, triangle ABC is an acute-angled triangle, not a right-angled triangle.

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