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Construct a triangle whose altitude is …

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Construct a triangle whose altitude is 2 cm and base angles are 45 and 60

    • Posted by Shilpa Choudhari 4 years, 10 months ago

    CBSE > Class 07 > Mathematics
    • 1 answers

    Sia ? 4 years, 10 months ago

    First of all, we draw a rough sketch.
    Let the required triangle be ABC in which base angles {tex}\angle{/tex}B = 45° and  {tex}\angle{/tex}C = 60°, altitude AD =  2 cm.
    Now, {tex}\angle{/tex}ADB = {tex}\angle{/tex}ADC = 90°
    In {tex}\triangle{/tex}ADB, {tex}\angle{/tex}BAD = 180° – ({tex}\angle{/tex}ABD + {tex}\angle{/tex}ADB)
    = 180° – (45° + 90°)
    = 180° – 135°
    = 45°
    In {tex}\triangle{/tex}ADC, {tex}\angle{/tex}CAD = 180° – ({tex}\angle{/tex}ACD + {tex}\angle{/tex}ADC)
    = 180° – (60° + 90°)
    = 180° – 150°
    = 30°
    Now, we construct two triangles having common base AD = 2cm

    {tex}\triangle{/tex}ABC is the required triangle whose altitude is 2 cm and base angles are 45° and  60°.

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