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7 December, 21:37

A right triangle has one angle that measure 23. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle?

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  1. 7 December, 23:35
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    Given for the Right Triangle:

    ∠A = 23°

    a (height) = 27.6cm

    c (hypotenuse) = 30cm

    Find:

    b (base) = ?

    Area of the Triangle = ?

    Solution:

    The formula for the area of triangle is: [ b*h]:2; where b is base and h is height

    Since you do not have the sides for the base, let's find it first before we can find the area.

    To find the b (base), we will use the law of cosine. Specifically the cos∠ = adjacent side:hypotenuse

    The ∠ that you should use is the angle that is adjacent to b (base) which is the ∠A

    That makes the law of cosine formula into: cos∠A = b:c

    Let's derive the formula to the side that we are looking for:

    Find a (height)

    b = cos∠A*c

    b = cos23 °*30cm; substituting the numbers

    b = 27.6151cm

    Now that there is a base, you can now find the area of the triangle.

    Area of Triangle = [b * h]:2

    Area of Triangle = [27.6151cm * 27.6cm]:2

    Area of Triangle = 381.0883cm ²; Final Answer
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