geometry

The lengths of segments PQ and PR are 8 inches and 5 inches, respectively, and they make a 60-degree angle at P.
(a) Find the area of triangle PQR.
(b) Find the length of the projection of segment PQ onto segment PR.
(c) Find the length of segment QR.

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  1. a) area = (1/2)(5)(8)sin60
    = ..

    b) the projection of PQ on PR = 5 cos 60
    = ...

    c) use the cosine law
    QR^2 = 5^2 + 8^2 - 2(5)(8)cos60
    = ...

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  2. Reiny,help, how do I find the following
    (d) Find the sizes of the other two angles of triangle PQR.
    (e) Find the length of the median drawn to side PQ.
    (f) Find the length of the bisector of angle R.
    (g) Find the third side of another triangle that has a 5-inch side, an 8-inch side, and the
    same area as triangle PQR

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  3. d) Use the Law of Sine in this question.
    7/sin60=5/sinQ=8/sinR
    Q=38.213, R=81.787

    f) The median bisects angle R, so half of angle R is 40.9 degrees. Taking the smaller triangle that contains P and R, we know the third angle of this triangle is 79.1. Then we can use the Law of Sine.
    bisector is 4.41 in

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