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In the given figure, AB=BC and angle BAC=15 degree, AB= 10 cm. Find the area of triangle ABC.?
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In the given figure, AB=BC and angle BAC=15 degree, AB= 10 cm. Find th...
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In the given figure, AB=BC and angle BAC=15 degree, AB= 10 cm. Find th...
Given: AB=BC=10cm, angle BAC=15 degree

To find: Area of triangle ABC

Solution:

  1. Find angle ABC: Since AB=BC, angle ABC=angle BAC=15 degree

  2. Find angle ACB: Since the angles of a triangle add up to 180 degree, angle ACB=180-15-15=150 degree

  3. Find height of triangle: Let the height of triangle ABC be h. Draw a perpendicular from point B to AC and let it meet AC at point D. Triangle ABD is a right angled triangle, therefore angle BAD=75 degree (half of angle BAC). Since AB=BD, angle ABD=angle BAD=75 degree. Therefore, angle BDC=180-75-75=30 degree. In triangle BDC, BD=h (as D is the midpoint of AC). Therefore, height of triangle ABC, h=BD=sin(30 degree) x BC=sin(30 degree) x 10=5 cm

  4. Find area of triangle ABC: Area of triangle ABC=1/2 x base x height=1/2 x AC x h=1/2 x 20 x 5=50 cm^2



Therefore, the area of triangle ABC is 50 cm^2.
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In the given figure, AB=BC and angle BAC=15 degree, AB= 10 cm. Find the area of triangle ABC.?
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