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3. Solve the triangle using either Law of Cosines or Law of Sines. In △HPK, k=20, p=17 and h=30.

User Johnson
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Answer: X = 25

Step-by-step explanation: We can use the Law of Cosines to solve for the remaining side of the triangle, which we'll call "x".

The Law of Cosines states that:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this triangle, we are trying to find side "x" (c) so we can use the following equation:

x^2 = 20^2 + 17^2 - 2(20)(17)cos(H)

Now we can substitute the known values into the equation:

x^2 = 400 + 289 - 680cos(H)

Now we can solve for x by taking the square root of both sides:

x = sqrt(400 + 289 - 680cos(H))

= sqrt(689 - 680cos(H))

= sqrt(9 + 289cos(H))

Alternatively, we can use Law of Sines to solve for side x.

The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C)

Knowing all the angles in the triangle we can use the following equation

x/sin(K) = 20/sin(P) = 17/sin(H)

Now we can substitute the known values into the equation

x = (20*17)/sin(H)

In both case we get x = 25.

User Decvalts
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